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ส า ร บั ญ หนา เรอ่ื ง 1 แผนการจดั การเรยี นรทู ่ี1 4 เรอื่ งการทดลองสมุ แซมเปล สเปซและเหตกุ ารณ ใบงานที่ 1 7 แผนการจดั การเรยี นรทู ี่2 10 เรอ่ื ง ความนา จะเปน เบอื้ งตน ใบงานที่ 2 13 แผนการจดั การเรยี นรทู ี่3 15 เรอื่ งความนา จะเปน โดยใชค วามรูเรอื่ งวธิ เี รยี งสบั เปลย่ี นและวธิ กี ารจดั หมู 19 ใบงานท่ี 3 แบบฝก หดั ที่1 20 แผนการจดั การเรยี นรทู ่ี4 22 เรอื่ ง ยเู นยี น อนิ เตอรเ ซกชนั คอมพลเี มนต และเหตกุ ารณท ไ่ี มเ กดิ รว มกนั 23 ใบงานที่ 4 แบบฝก หดั ท่ี2 25 แผนการจดั การเรยี นรทู ่ี5 27 เรอื่ ง ความนา จะเปน โดยใชค วามรูเรอ่ื ง ยเู นยี น อนิ เตอรเ ซกชนั คอมพลเี มนต 29 ใบงานท่ี 5 แบบฝก หดั ท่ี3 30 แผนการจดั การเรยี นรทู ่ี6 32 เรอื่ ง กฎทส่ี ำคญั บางประการเกยี่ วกบั ความนา จะเปน 35 ใบงานที่ 6 แบบฝก หดั ท่ี4 37 แผนการจดั การเรยี นรทู ี่7 39 เรอ่ื งโจทยป ญ หาความนา จะเปน 40 ใบงานที่ 7 แบบฝก ทกั ษะ

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2 ⌫ ⌫  ⌦  ⌫      2. ‹ŠÁ…¸¥œÂŽ¤Áž¨d ­ÁžŽ‹µ„„µ¦Ã¥œÁ®¦¥¸  1 °´œ 2 ‡¦ŠÊ´ ×¥­œÄ‹®œµo …°ŠÁ®¦¥¸ šÉ¸Á„·—…¹œÊ ‹³Å—o S = {HH, HT, TH, TT} n(S) = 4 3. ‹ŠÁ…¥¸ œÂŽ¤Áž¨d ­ÁžŽ‹µ„„µ¦Ã¥œ¨¼„Á˜qµ 1 ¨„¼ 1 ‡¦ÊŠ´ ×¥­œÄ‹Â˜o¤…°Š¨„¼ Á˜qµšÉ¸Á„—· …¹œÊ ‹³Å—o S = {1, 2, 3, 4, 5, 6} n(S) = 6 4. ‹ŠÁ…¸¥œÂŽ¤Ážd¨­ÁžŽ‹µ„„µ¦Ã¥œ¨„¼ Á˜µq 1 ¨¼„ 2 ‡¦ÊŠ´ ×¥­œÄ‹Â˜o¤…°Š¨„¼ Á˜qµšÊ´Š­°Š‡¦ÊŠ´ ‹³Å—o S = {(1, 1), (1, 2), (1, 3), . . . , (6, 6)} n(S) = 6 u 6 = 36 5. ‹ŠÁ…¸¥œ‹ÎµœªœŸ¨¨´¡›šr ʊ´ ®¤—…°Š„µ¦š—¨°Š­n¤» ¨„¼ °¨ 3 ¨„¼ ‹µ„¨„¼ °¨­˜¸ nµŠ„´œ 10 ¨¼„ n(S) = §©¨¨130 ·¹¸¸ 6. ‹ŠÁ…¥¸ œ‹µÎ œªœŸ¨¨´¡›rš´ÊŠ®¤—…°Š„µ¦š—¨°Š­¤n» Á¨°º „œ„´ Á¦¥¸ œµ¥ 1 ‡œ ¨³œ„´ Á¦¥¸ œ®Š· 1 ‡œ ‹µ„œ„´ Á¦¸¥œµ¥ 4 ‡œ ¨³œ„´ Á¦¥¸ œ®Š· 5 ‡œ n(S) = §¨©¨ 4 ¸·¸¹ u §¨©¨15 ¸·¹¸ 1 7. „¨n°ŠÄ®œŠ¹É ¤¨¸ ¼„°¨­¸Â—Š 3 ¨„¼ ­¸…µª 4 ¨„¼ ­œ¸ µÎÊ ÁŠ·œ 5 ¨¼„ ץ˜¨n ³¨„¼ ¤¸…œµ—Ášµn „´œ ­n»¤®¥·¨„¼ °¨Äœ„¨°n Šœ¸Ê¤µ 3 ¨¼„ ‹Š®µ n(S) n(S) = §©¨¨132 ¹·¸¸ 8. ‹ŠÁ…¸¥œÁ®˜„» µ¦–r ‹µ„„µ¦Ã¥œ¨„¼ Á˜qµ 2 ¨„¼ 1 ‡¦´ÊŠ ­œÄ‹šÂ¸É ˜o¤¦ª¤…°Š¨¼„Á˜µq Áž}œ 6 ‹³Å—o E = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)} n(S) = 5 9. „¨°n ŠÄ®œÉ¹Š¤¸¨¼„°¨­¸Â—Š 3 ¨„¼ ­¸…µª 4 ¨„¼ ­œ¸ ÎµÊ ÁŠœ· 5 ¨¼„ ץ˜¨n ³¨¼„¤…¸ œµ—Ášµn „œ´ ­¤n» ®¥· ¨¼„°¨Äœ„¨n°Šœ¸¤Ê µ 3 ¨¼„ ‹Š®µ n(A) Á¤°Éº A šœÁ®˜„» µ¦–šr ɸ­n¤» ®¥· ŗo¨„¼ °¨šŠ´Ê 3 ¨„¼ ¤­¸ ¸˜µn Š„œ´ n(A) = §¨¨©13 ¸¸¹· §¨¨© 4 ¸¸¹· ¨¨§©15 ¸¸¹· = 60 1 10. „¨°n ŠÄ®œŠÉ¹ ¤¨¸ ¼„°¨­¸Â—Š 3 ¨¼„ ­…¸ µª 4 ¨„¼ ­¸œÎµÊ ÁŠ·œ 5 ¨„¼ ץ˜¨n ³¨¼„¤…¸ œµ—Ášnµ„´œ ­n¤» ®¥· ¨¼„°¨Äœ„¨n°Šœ¸Ê¤µ 3 ¨¼„ ‹Š®µ n(B) Á¤ºÉ° B šœÁ®˜„» µ¦–šr É­¸ »¤n ®¥· ŗo¨„¼ °¨šÊ´Š 3 ¨„¼ ¤¸­Á¸ ®¤º°œ„œ´ n(B) = §¨©¨ 3 ·¸¹¸ + ©¨§¨ 4 ¹·¸¸ + ¨¨§©53¸¹¸· = 15 3 3

⌦ 3 ⌦ 4.3 Ä®œo „´ Á¦¸¥œšÎµÄŠµœšÉ¸ 1 ¨³˜¦ª‹­°‡ªµ¤™„¼ ˜°o Š…°ŠÄŠµœš¸É 1 4.4 œ„´ Á¦¥¸ œ­¦ž» ŗoªµn ‹Îµœªœ­¤µ·„…°ŠÂŽ¤Ážd¨­ÁžŽ n(S) ‡º° ‹Îµœªœª›· ¸…°ŠÁ®˜»„µ¦–ršÁɸ „—· °¥nµŠÅ¤¤n Á¸ Š°ºÉ œÅ… ¨³‹Îµœªœª›· …¸ °ŠÁ®˜„» µ¦–r n(E) ‡°º ‹Îµœªœª›· …¸ °ŠÁ®˜»„µ¦–šr ¸ÁÉ „—· …ʹœ°¥nµŠ¤Á¸ Š°Éº œÅ… ŽÉ¹ŠÁžœ} Á®˜„» µ¦–šr Áɸ žœ} ­´ ÁŽ˜…°ŠÂŽ¤Áž¨d ­ÁžŽ 5. ®¨Šn Á¦¥¸ œ¦¼o 5.1 ®°o Š­¤»— ®œ´Š­°º Á¦¸¥œ ®œŠ´ ­°º °nµœž¦³„°š¸ÉÁ„ɸ¥ª„´ Á¦°Éº Š‡ªµ¤œnµ‹³Ážœ} 5.2 ĝŠµœš¸É 1 6. „¦³ªœ„µ¦ª´—Ÿ¨ž¦³Á¤œ· Ÿ¨ „µ¦ž¦³Á¤œ· Ÿ¨ „µ¦ª—´ Ÿ¨ 1. œ´„Á¦¸¥œ Ť¦n nª¤„‹· „¦¦¤ ˜°o Šž¦´ž¦»Š 1. ­Š´ Á„˜„µ¦¦ªn ¤„·‹„¦¦¤…°Šœ„´ Á¦¥¸ œ ¦nª¤„‹· „¦¦¤ —¸ 2. œ´„Á¦¥¸ œ šµÎ ŗo 1 – 4 …°o ˜°o Šž¦´ ž¦»Š 2. ĝŠµœšÉ¸ 1 šµÎ ŗo 5 – 6 …o° —¸ šµÎ ŗo 7 – 8 …°o —¸¤µ„ 7. ´œš„¹ ®¨Š´ ­°œ ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… 8. „·‹„¦¦¤Á­œ°Âœ³ ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ………………………………………………………………………………………………………………

4 ⌫ ⌫  ⌦  ⌫      ĝŠµœš¸É 1 ‡µÎ Â¸Ê ‹Š œ„´ Á¦¸¥œ°nµœÂ¨³Á˜¤· ‡Îµ˜°¨ŠÄœ°n Š „µ¦š—¨°ŠÁŠ· ­¤n» (Random Experiment ) ®¤µ¥™¹Š „µ¦š—¨°ŠŽÉ¹ŠÅ¤n­µ¤µ¦™šµÎ œµ¥Ÿ¨¨¡´ ›r …°Š„µ¦š—¨°ŠÅ—°o ¥nµŠÂœœn °œ Á¡¥¸ ŠÂ˜šn ¦µªnµ Ÿ¨¨´¡›°r µ‹‹³Ážœ} °³Å¦Å—o µo Š ŽÉ¹ŠÁŽ˜…°ŠŸ¨¨¡´ ›ršÉ¸ Ážœ} Şŗoš´ŠÊ ®¤—…°Š„µ¦š—¨°ŠÁ·Š­»¤n Á¦¸¥„ªµn Ž¤Áž¨d ­ÁžŽ ( Sample Space ) ×¥šªÉ´ ŞÁ…¥¸ œÂšœ —ªo ¥ S Á®˜„» µ¦–r (Event) ‡°º ­´ÁŽ˜…°ŠÂŽ¤Áž¨d ­ÁžŽ —Š´ œœ´Ê ÁŽ˜ªnµŠ„ȇ°º Á®˜»„µ¦–®r œÉ¹ŠÁnœ„œ´ ™oµ S Áž}œÁŽ˜‹Îµ„—´ ¨³ E šœÁŽ˜…°ŠÁ®˜„» µ¦–r ¨oª ‹³Å—ªo µn 1. E Ážœ} ÁŽ˜‹Îµ„´— 2. 0 d n(E) d n(S) 3. n(E) = n(S) Á¤É°º S = E 1. ‹µ„„µ¦Ã¥œ¨„¼ Á˜µq ­°Š¨¼„¡¦°o ¤„œ´ œ„´ Á¦¸¥œ‹³¡ªµn ˜o¤…°Š¨„¼ Á˜µq ‹³…¹Êœ®œoµ˜µn ŠÇ „´œ—Š´ œÊ¸ 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 51 52 53 54 55 56 61 62 63 64 65 66 ŽŠÉ¹ ‹µ„Á®˜„» µ¦–šr Š´Ê ®¤—œÊ¸Á¦¥¸ „ªnµÂŽ¤Áž¨d ­ÁžŽ ¤š¸ ŠÊ´ ®¤— 36 Á®˜„» µ¦–r ‹Š®µÁŽ˜Â¨³‹µÎ œªœ­¤µ·„…°Š Á®˜„» µ¦–r˜°n Şœ¸Ê (Á…¥¸ œÄœ¦ž¼ ÁŽ˜‡°n¼ ´œ—´ Ž¹ÉŠ­¤µ·„˜´ª®œµo …°Š‡n¼°œ´ —´Ážœ} ˜¤o …°Š¨„¼ Á˜qµ¨„¼ š®É¸ œŠ¹É ¨³ ­¤µ„· ˜ª´ ®¨Š´ Áž}œÂ˜o¤…°Š¨„¼ Á˜µq ¨¼„šÉ¸­°Š) 1.1 E : šœÁŽ˜…°ŠÁ®˜„» µ¦–šr Åɸ —Âo ˜¤o ˜¦Š„´œ E =……………………………………...…………………….…………………………… n (E) = …..………………………………………………………………………………...… 1.2 E1 : šœÁŽ˜…°ŠÁ®˜„» µ¦–ršÅɸ —Âo ˜¤o ˜nµŠ„œ´ E1 = …….…………………………………………………………….…….……………. n (E1) = ……..……………………………………………………………..….………………

⌦ 5 ⌦ 1.3 E2 : šœÁŽ˜…°ŠÁ®˜„» µ¦–ršÉ¸Å—Ÿo ¨¦ª¤…°ŠÂ˜¤o Ášnµ„´ 10 E2 = …………………………………….…………………………………..……………. n (E2) = ………….…………………….……………………………………….……………... 1.4 E3 : šœÁŽ˜…°ŠÁ®˜»„µ¦–šr ɸŗoŸ¨¦ª¤…°ŠÂ˜¤o Ášµn „´ 10 ®¦º°¨¼„Á˜µq š´ŠÊ ­°Š…œÊ¹ ®œoµ˜¦Š„´œ E3 = ……………………………………………………………….…………..……........... n (E3) = ……………………………………………………………………….….…………... 1.5 E4 : šœÁŽ˜…°ŠÁ®˜„» µ¦–šr ¸ÉŗŸo ¨¦ª¤…°ŠÂ˜¤o ¤µ„„ªµn 10 E4 = ………………………………………………………………………….….…….…. n (E4) = ………..……...……………………………………………..……………..………… 1.6 E5 : šœÁŽ˜…°ŠÁ®˜„» µ¦–ršÉŸ¸ ¨¦ª¤…°ŠÂ˜¤o ¤µ„„ªnµ®¦°º Ášnµ„´ 10 E5 = …………………………………………………………. …………….……...…...… n (E5) = ………….……….………...………………………………..……………..………… 1.7 E6 : šœÁŽ˜…°ŠÁ®˜„» µ¦–ršŸ¸É ¨¦ª¤…°ŠÂ˜o¤Ášnµ„´ 6 E6 = ………………………………………………….………………..………….............. n (E6) = ………….………………………………………..……….……………………..…... 1.8 E7 : šœÁŽ˜…°ŠÁ®˜„» µ¦–šr ¸ÉŸ¨¦ª¤…°ŠÂ˜o¤Ášnµ„´ 8 E7 = …………………………………………………… ….…………………………....... n (E7) = …………..…………………………………………………..…………………..…… 2. ‡¦°‡¦´ª®œÉ¹Š¤¸»˜¦ 3 ‡œ ‹Š®µÁŽ˜Â¨³‹µÎ œªœ­¤µ„· …°ŠÁŽ˜˜°n Şœ¸Ê 2.1 E1 : šœÁŽ˜…°ŠÁ®˜»„µ¦–šr Å¸É —o ˜» ¦µ¥ 3 ‡œ E1 = ……………………....…………………………………………..………………...… n (E1) = ……………………………………………………………………….……................ 2.2 S : šœÁŽ˜…°ŠÂŽ¤Ážd¨­ÁžŽ S = ……………………………………………………………………..….………...……. n (S) = .…………..………………………………………………………..………................. 2.3 A : šœÁŽ˜…°ŠÁ®˜»„µ¦–šr ¤É¸ ¸ »˜¦µ¥°¥nµŠ¤µ„ 2 ‡œ A = …………………………………………………..………….……………................. n (A) = ………….……………………………………………………………………………

6 ⌫ ⌫  ⌦  ⌫      2.4 B : šœÁŽ˜…°ŠÁ®˜»„µ¦–rš¤¸É ¸ ˜» ¦­µª°¥µn Šœ°o ¥ 2 ‡œ B = ……………………………………………………………………………..………... n (B) = ………….…………………………………………………….…………..……......... 3. „¨n°ŠÄ®œ¹ÉŠ¤¨¸ „¼ °¨­Â¸ —Š 3 ¨¼„ ­¸…µª 4 ¨¼„ ­¸œÎʵÁŠ·œ 5 ¨¼„ ץ˜n¨³¨„¼ ¤…¸ œµ—˜nµŠ„œ´ ­¤»n ®¥· ¨¼„°¨ 3 ¨¼„˜°o Š„µ¦Ä®oŗ¨o „¼ °¨š´ŠÊ 3 ¨„¼ ¤­¸ ˜¸ µn Š„œ´ ‹Š®µ n (E) = …………………………………..………………………………………………….. n (S) = …………………….……………………………………………………………...… 4. „¨°n ŠÄ®œÉ¹Š¤¸¨„¼ °¨­Â¸ —Š 3 ¨„¼ ­…¸ µª 4 ¨„¼ ­¸œµÎÊ ÁŠœ· 5 ¨„¼ ץ˜n¨³¨„¼ ¤…¸ œµ—˜µn Š„œ´ ­n»¤®¥· ¨„¼ °¨ 3 ¨¼„˜°o Š„µ¦Ä®Åo —¨o „¼ °¨¤­¸ Á¸ ®¤°º œ„œ´ š´ÊŠ 3 ¨¼„ ‹Š®µ n (E) = ………………………………………………..………………………………...…… n (S) = ………………………………………………………………………........................ 5. č„o ¦³™µŠ—µªÁ¦º°Š 3 „¦³™µŠ „¦³™µŠ„®» ¨µ 4 „¦³™µŠ ˜Šn ÁªšÁ¸ žœ} ªŠ„¨¤ ץč˜o œo Ťo 1 „¦³™µŠ ªµŠ„¨µŠÁªš¸ ¨³„¦³™µŠ˜œo Ťoš¸ÁÉ ®¨º°ªµŠ¦°Ç Áªš¸ ˜°o Š„µ¦Ä®o„»®¨µ°¥„¼n ¨µŠÁªš¸ ¨³˜oœÅ¤ošÉ¸ Á®¨º°ªµŠ­¨´¦°Ç Áªš¸ ‹Š®µ n (E) = …………………...………..………………………………………………………… n (S) = ……………..…………….…………………………………………………...……... 6. Ĝ„µ¦ÂŠn Ÿ¼o µ¥ 5 ‡œ ¨³Ÿo¼®Š· 3 ‡œ Á…µo ¡„´ ®°o Š¡„´ 3 ®°o Š ×¥¤¸®o°ŠÇ ®œ¹ÉŠ¡´„Å—o Á¡¸¥Š 2 ‡œ ­nªœ°„¸ 2 ®o°Š ¡´„Å—®o °o Š¨³ 3 ‡œ ˜°o Š„µ¦Ä®oŸo¼®·Š 3 ‡œÅ—¡o „´ ®°o ŠÁ—¸¥ª„œ´ ‹Š®µ n (E) = ………………………..…………….………..……………………………………… n (S) = ………………………….…………………………………………………………… 7. ¤¸­µ¤Á–¦ 1 ¦ž¼ Ÿ®¼o Š· 3 ‡œ µ¥ 2 ‡œ ‹—´ ‡œšÊŠ´ ®¤—œ´ÉŠÁ„oµ°¸Ê ĜœªÁ­oœ˜¦Š „µÎ ®œ—Ä®o E šœ ÁŽ˜…°ŠÁ®˜»„µ¦–r šÉ‹¸ ´—Å—­o µ¤Á–¦œ´ÉŠÅ¤˜n —· „´ Ÿo¼®·Š ‹Š®µ n (E) = …………………………………….………………………………………………… n (S) = ……………………..….…………………………………………………………….. 8. ¤¸®¨°—Å¢ 15 ®¨°—Äœ‹µÎ œªœœÊ¸ ¤¸®¨°—Á­¸¥ 5 ®¨°— ™oµ­n»¤®¥·®¨°—Å¢¤µ 3 ®¨°— „ε®œ— E šœ ÁŽ˜…°ŠÁ®˜„» µ¦–ršÉ®¸ ¥· ŗ®o ¨°——°¸ ¥µn Šœo°¥ 1 ®¨°— ‹Š®µ n (E) = ……..…………………………………………….…………………..………………. n (S) = …..…….……………………..……………………………………………………….

⌦ 7 ⌦ Ÿœ„µ¦‹—´ „µ¦Á¦¥¸ œ¦šo¼ ɸ 2 Á¦°Éº Š ‡ªµ¤œnµ‹³Áž}œÁÊ°º Š˜œo œÊ´ ¤›´ ¥¤«¹„¬µžše ɸ 6 ª· µ ‡–˜· «µ­˜¦r Áª¨µ 3 Éª´ äŠ Ÿ¨„µ¦Á¦¥¸ œ¦šo¼ ɸ‡µ—®ªŠ´ œ´„Á¦¥¸ œ­µ¤µ¦™Â„žo {®µÃ‹š¥Ár ¦ºÉ°Š‡ªµ¤œµn ‹³Ážœ} ŗo 1. ‹—» ž¦³­Š‡„r µ¦Á¦¥¸ œ¦¼o 1.1 ®µ‹Îµœªœ­¤µ·„…°ŠÂŽ¤Áž¨d ­ÁžŽ 1.2 ®µ‹Îµœªœ­¤µ·„…°ŠÁ®˜»„µ¦–rŗo 1.3 ®µ‡ªµ¤œnµ‹³Ážœ} ŗo 2. œª‡ªµ¤‡—· ®¨´„ ค‡วªาµม¤นœา µn จ‹ะ³เปÁžน œ} คอ‡ื °º อตั °ร´˜าส¦วµ ­นnªระœห¦ว³า®งªจµnำนŠ‹วµÎนœสªมœา­ชก¤ิ ขµอง„· เ…ห°ตŠกุ Áา®ร˜ณ„» ก µบั ¦จ–ำrนวน„´สม‹µÎาชœกิªขœอ­ง¤แµซม·„เป…ล°สŠเÂปŽซ¤ ทÁžแี่ ¨d ส­ดÁงžใŽหท ราบšว¸ÂÉ า ­เห—ตŠกุÄา®รošณ¦ใ µดเหªµnตÁ®กุ า˜ร„» ณµห¦ –นÄrงึ่ —มÁโี®อ˜ก„» าสµ¦เก–ดิ ®r ขœนึ้ ŠÉ¹ ไ¤ดøม °า„กµน­อ Á„ยเ—·พ…ยี œÊ¹งใÅด—ซo¤ง่ึµช„วœย°o ใ¥นÁก¡า¥¸ รŠคÄดิ—แŽลŠÉ¹ ะตªn ดั¥สĜนิ „ใµจ¦ ท‡·—ำใÂห¨ม ³กี ˜า—´ร­วาœ· งÄแ‹ผนšลεวÄง®หo¤น¸„าµ¦ªµŠÂŸœ¨ªn Š®œµo 3. Áœº°Ê ®µ­µ¦³ ™oµ N Áž}œ‹µÎ œªœ­¤µ·„…°ŠÂŽ¤Ážd¨­ÁžŽ S ŽÉŠ¹ ž¦³„°—ªo ¥‹Îµœªœ­¤µ„· šÉ¸¤Ã¸ °„µ­Á„·—…¹œÊ ŗoÁšµn Ç „œ´ ¨³ n Áž}œ‹µÎ œªœ­¤µ·„…°ŠÁ®˜„» µ¦–r E ŽÉŠ¹ Áž}œ­´ ÁŽ˜…°Š S ¨ªo ‡ªµ¤œnµ‹³Ážœ} …°Š Á®˜„» µ¦–r E Ášnµ„´ n ¨³Á…¥¸ œ P(E) šœ‡ªµ¤œµn ‹³Ážœ} …°ŠÁ®˜»„µ¦–r E N P(E) = n(E) = n n(S) N ¨³ 0 d P(E) d 1

8 ⌫ ⌫  ⌦  ⌫      4. „¦³ªœ„µ¦‹—´ „µ¦Á¦¸¥œ¦¼o 4.1 ‡¦¼¡—¼ ‡»¥„´œ´„Á¦¥¸ œ™Š¹ Á¦Éº°Š‡ªµ¤œnµ‹³Áž}œ ŽÉ¹Šœ„´ Á¦¸¥œÅ—oÁ¦¥¸ œ¤µoµŠÂ¨oªÄœœ´Ê ¤´›¥¤«„¹ ¬µžše ¸É 3 ‡ªµ¤®¤µ¥…°Š‡ªµ¤œµn ‹³Ážœ} Ĝœ´Ê œ¥¸Ê Š´ ‡ŠÁ®¤°º œÁ—¤· ˜¥n µ„…¹œÊ Á¡¦µ³˜°o ŠÄ‡o ªµ¤¦Áo¼ ¦ºÉ°Š „µ¦Á¦¥¸ Š­´ Áž¨¥¸É œ ¨³ª›· ¸‹—´ ®¤Ä¼n œ„µ¦®µ‹µÎ œªœ­¤µ·„…°ŠÂŽ¤Áž¨d ­ÁžŽ ¨³‹µÎ œªœ­¤µ·„…°ŠÁ®˜„» µ¦–r 4.2 Ä®oœ„´ Á¦¥¸ œ«„¹ ¬µ‹µ„˜ª´ °¥nµŠ˜°n ޜʸ 1. ‹µ„„µ¦Ã¥œÁ®¦¥¸  1 °´œ 1 ‡¦ÊŠ´ ×¥­œÄ‹®œoµ…°ŠÁ®¦¥¸ šÉ¸Á„—· …¹œÊ ‹Š®µ‡ªµ¤œµn ‹³Ážœ} …°ŠÁ®˜»„µ¦–rš¸ÉÁ®¦¥¸ …ʹœ®´ª ‹³Å—o S = {H, T} E = {H} P(E) = n(E) = 1 n(S) 2 2. ‹µ„„µ¦Ã¥œ¨„¼ Á˜µq 1 ¨¼„ 1 ‡¦Š´Ê ‹Š®µ‡ªµ¤œµn ‹³Áž}œšÉ¨¸ „¼ Á˜µq …œÊ¹ ˜¤o ‡n¼ ‹³Å—o S = {1, 2, 3, 4, 5, 6} E = {2, 4, 6} P(E) = n(E) = 3 = 1 n(S) 6 2 3. ‡¦°‡¦ª´ ®œ¹ÉŠ¤¸˜» ¦ 3 ‡œ ‹Š®µ‡ªµ¤œµn ‹³Ážœ} š¸É¤¸ ˜» ¦µ¥°¥µn Šœo°¥ 2 ‡œ ‹³Å—o S = {, , , , , , , } E = {, , ,  } P(E) = n(E) = 4 = 1 n(S) 8 2 4. „¨n°ŠÄ®œÉŠ¹ ¤¸¨¼„°¨­Â¸ —Š 3 ¨¼„ ­…¸ µª 4 ¨„¼ ­œ¸ µÎÊ ÁŠ·œ 5 ¨¼„ ץ˜¨n ³¨„¼ ¤…¸ œµ— Ášµn „œ´ ­»¤n ®¥· ¨¼„°¨Äœ„¨°n Šœ¤Ê¸ µ 3 ¨¼„ ‹Š®µ P(B) Á¤É°º B šœÁ®˜»„µ¦–rš­¸É »¤n ®¥· ŗo¨„¼ °¨šÊŠ´ 3 ¨„¼ ¤­¸ Á¸ ®¤º°œ„œ´ n(B) = §©¨¨33 ¸·¸¹ + ©§¨¨ 4 ¸¸¹· + ¨©§¨ 5 ·¸¸¹ = 15 3 3 n(S) = ¨©¨§132 ¹¸¸· = 220 P(B) = n(B) = 15 = 3 n(S) 220 44 4.3 Ä®œo „´ Á¦¥¸ œšÎµÄŠµœšÉ¸ 2 ×¥‡¦¼—¼ ¨ ¨³°›·µ¥Â„Åo ……o°„¡¦°n Š…°Šœ„´ Á¦¥¸ œÂ˜¨n ³‡œ 4.4 œ„´ Á¦¥¸ œ­¦»žÅ—oªµn P(E) = n(E) = n ×¥š¸É 0d P(E) d 1 ¨³ ™oµ‡nµ…°Š n n(S) N N ¤¸‡nµÁ…oµÄ„¨o 1 ¤µ„Ç ®¤µ¥‡ªµ¤ªµn Á®˜„» µ¦–rœœÊ´ ¤Ã¸ °„µ­Á„—· …œÊ¹ ŗo­¼Š¤µ„ ™µo ‡µn …°Š n ¤¸‡nµÁ…oµÄ„¨o 0 ¤µ„Ç N ®¤µ¥‡ªµ¤ªnµ Á®˜„» µ¦–rœœÊ´ ¤Ã¸ °„µ­Á„·—…œ¹Ê ŗœo o°¥¤µ„

⌦ 9 ⌦ 5. ®¨Šn Á¦¥¸ œ¦¼o „µ¦ž¦³Á¤·œŸ¨ 5.1 ĝŠµœš¸É 2 1. œ´„Á¦¸¥œ Ťn¦ªn ¤„·‹„¦¦¤ ˜o°Šž¦´ž¦»Š 5.2  f„®—´ š¸É 1 ¦ªn ¤„‹· „¦¦¤ —¸ 6. „¦³ªœ„µ¦ª—´ Ÿ¨ž¦³Á¤œ· Ÿ¨ 2. œ´„Á¦¸¥œ šÎµÅ—o 1 – 4 …°o ˜o°Šž¦´ ž¦Š» „µ¦ª—´ Ÿ¨ šÎµÅ—o 5 – 8 …°o —¸ 1. ­´ŠÁ„˜„µ¦¦nª¤„·‹„¦¦¤…°Šœ„´ Á¦¸¥œ šÎµÅ—o 9 – 10 …o° —¤¸ µ„ 2. ĝŠµœš¸É 2 7. ´œš„¹ ®¨Š´ ­°œ ……………………………………………………………………………………………………………..… …….……...………………………………………………………………………………………………..… ……………..……...……………………………………………………………………………………….… ……………………..………….…………………………………………………………………………...… ……………………..………….…………………………………………………………………………...… 8. „‹· „¦¦¤Á­œ°Âœ³ ……………………………………………………………………………………………………………..… …….……...………………………………………………………………………………………………..… ……………..……...……………………………………………………………………………………….… ……………………..………….…………………………………………………………………………...… ……………………..………….…………………………………………………………………………...…

10 ⌫ ⌫  ⌦  ⌫      ĝŠµœšÉ¸ 2 ‡µÎ Â¸Ê ‹Š œ´„Á¦¸¥œ°µn œÄœ„¦°­Áɸ ®¨É¥¸ ¤ ¨oª‹ŠÁ˜¤· ‡µÎ ˜°Äœn°Šªµn Š P(E) = n(E) = n n(S) N ¨³ 0 d P(E) d 1 1. ‹µ„„µ¦Ã¥œ¨„¼ Á˜µq 2 ¨¼„šÂɸ ˜„˜µn Š„œ´ ‹Š®µ‡ªµ¤œnµ‹³Ážœ} …°ŠÁ®˜„» µ¦–r˜n°ÅžœÊ¸ 1.1 ŗŸo ¨¦ª¤…°ŠÂ˜o¤Ášµn „´ 10 ®¦°º …¹ÊœÂ˜¤o Á®¤°º œ„œ´ š´ŠÊ 2 ¨¼„ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 1.2 Ÿ¨¦ª¤…°ŠÂ˜¤o Ážœ} ‹Îµœªœ‡¼n ®¦º° ¨„¼ ®œ¹ÉŠ…œÊ¹ ˜o¤ 6 n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 1.3 Ÿ¨¦ª¤…°ŠÂ˜¤o …°Š¨¼„Á˜µq Áž}œ 8 n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 1.4 šÉ¸Ÿ¨¦ª¤…°Š¨„¼ Á˜qµš´ÊŠ­°Š¨„¼ Ášµn „´ 7 ®¦°º …ʹœÂ˜¤o 4 °¥nµŠœ°o ¥ 1 ¨„¼ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 2. ‡¦°‡¦ª´ ®œŠ¹É ¤¸ »˜¦ 3 ‡œ ‹Š®µ‡ªµ¤œnµ‹³Ážœ} …°ŠÁ®˜„» µ¦–ršÅ¸É —o »˜¦µ¥°¥µn Šœ°o ¥ 2 ‡œ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 3. Ã¥œ¨„¼ Á˜qµ 2 ¨„¼ ¡¦°o ¤„œ´ ‹Š®µ‡ªµ¤œnµ‹³Áž}œš¸ÉŸ¨¦ª¤…°Š¨¼„Á˜qµšÊ´Š­°Š¨¼„Ášnµ„´ 8 ®¦°º …œ¹Ê ˜o¤ 6 °¥µn Šœ°o ¥ 1 ¨„¼ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........

⌦ 11 ⌦ 4. Ĝ„µ¦Á¨°º „‹µÎ œªœÁ˜¤È ¤µ 1 ‹µÎ œªœ ‹µ„‹µÎ œªœÁ˜È¤˜Ê´ŠÂ˜n 10 ™¹Š 49 ‹Š®µ‡ªµ¤œnµ‹³Áž}œšÁɸ ¨… ‹µÎ œªœœœÊ´ ®µ¦—oª¥ 7 ¨Š˜´ª ®¦°º Áž}œ‹µÎ œªœ‡¼n n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 5. ¤­¸ µ¤Á–¦ 1 ¦¼ž Ÿ¼®o Š· 3 ‡œ µ¥ 2 ‡œ ‹´—‡œšŠ´Ê ®¤—œŠ´É Á„µo °Ê¸ ĜœªÁ­œo ˜¦Š ‹Š®µ‡ªµ¤œµn ‹³Ážœ} …°Š Á®˜„» µ¦–šr ¸‹É ´—Å—­o µ¤Á–¦œŠÉ´ Ťn˜—· Ÿ¼o®·Š n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 6. ¤®¸ ¨°—Å¢ 15 ®¨°— Ĝ‹µÎ œªœœÊ¤¸ ¸®¨°—Á­¸¥ 5 ®¨°— ™oµ­¤»n ®¥·®¨°—Å¢°°„¤µ 3 ®¨°— ‹Š®µ‡ªµ¤ œµn ‹³Ážœ} …°ŠÁ®˜»„µ¦–˜r n°ÅžœÊ¸ 6.1 ŗo®¨°——¸°¥nµŠœ°o ¥ 1 ®¨°— n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 6.2 ŗo®¨°—Á­¸¥°¥nµŠœo°¥ 1 ®¨°— n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 7. ‡¦°‡¦ª´ ®œŠÉ¹ ¤¸ ˜» ¦ 3 ‡œ ‹Š®µ‡ªµ¤œµn ‹³Ážœ} …°ŠÁ®˜»„µ¦–šr Åɸ —o ˜» ¦µ¥°¥µn Š¤µ„ 2 ‡œ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 8. „¨°n ŠÄ®œ¹ÉŠ¤¸¨„¼ °¨­Â¸ —Š 3 ¨¼„ ­¸…µª 4 ¨¼„ ­œ¸ µÎÊ ÁŠ·œ 5 ¨„¼ ץ˜¨n ³¨„¼ ¤…¸ œµ—˜µn Š„œ´ ­»¤n ®¥·¨¼„ °¨ 3 ¨„¼ ‹Š®µ‡ªµ¤œnµ‹³Áž}œšÉ¸®¥·Å—¨o „¼ °¨šÊ´Š 3 ¨¼„¤­¸ ˜¸ nµŠ„œ´ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........

12 ⌫ ⌫  ⌦  ⌫      9. „¨°n ŠÄ®œÉ¹Š¤¸¨„¼ °¨­Â¸ —Š 3 ¨¼„ ­…¸ µª 4 ¨¼„ ­¸œµÎÊ ÁŠœ· 5 ¨¼„ ץ˜n¨³¨„¼ ¤…¸ œµ—˜µn Š„œ´ ­n»¤®¥· ¨¼„ °¨ 3 ¨¼„ ‹Š®µ‡ªµ¤œnµ‹³Ážœ} š®É¸ ¥·Å—o¨„¼ °¨¤­¸ ¸Á®¤°º œ„œ´ šÊŠ´ 3 ¨¼„ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 10. čo„¦³™µŠ—µªÁ¦°º Š 3 „¦³™µŠ „¦³™µŠ„»®¨µ 4 „¦³™µŠ ˜nŠÁªšÁ¸ ž}œªŠ„¨¤ ץčo˜œo Ťo 1 „¦³™µŠ ªµŠ„¨µŠÁªš¸ ¨³„¦³™µŠ˜œo Ťšo ÉÁ¸ ®¨º°ªµŠ¦°Ç Áªš¸ ªµŠ­¨´ ¦°Ç Áªš¸ ‹Š®µ‡ªµ¤œµn Ážœ} …°Š Á®˜„» µ¦–ršÉ¸‹³Å—„o ¦³™µŠ„®» ¨µ°¥„¼n ¨µŠÁªš¸ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........

⌦ 13 ⌦ Ÿœ„µ¦‹´—„µ¦Á¦¸¥œ¦¼šo ɸ 3 Á¦º°É Š ‡ªµ¤œnµ‹³Ážœ} ץč‡o ªµ¤¦o¼ Á¦°ºÉ Š ª›· Á¸ ¦¸¥Š­´Áž¨¥¸É œ ¨³ª·›„¸ µ¦‹—´ ®¤¼n œ´Ê ¤´›¥¤«¹„¬µžeš¸É 6 ª·µ ‡–·˜«µ­˜¦r Áª¨µ 3 ´ÉªÃ¤Š Ÿ¨„µ¦Á¦¸¥œ¦šo¼ ¸‡É µ—®ª´Š œ„´ Á¦¥¸ œ­µ¤µ¦™Â„žo { ®µÃ‹š¥r Á¦Éº°Š ‡ªµ¤œnµ‹³Ážœ} ŗo 1. ‹»—ž¦³­Š‡„r µ¦Á¦¥¸ œ¦¼o 1.1 œ„´ Á¦¥¸ œÄ‡o ªµ¤¦o¼ Á¦°Éº Š ª›· ¸Á¦¥¸ Š­´Áž¨¥¸É œ ¨³ª·›„¸ µ¦‹´—®¤n¼ ®µ‹µÎ œªœ­¤µ„· …°ŠÁ®˜„» µ¦–År —o 1.2 œ„´ Á¦¥¸ œÄ‡o ªµ¤¦¼o Á¦ºÉ°Š ª›· ¸Á¦¥¸ Š­´Áž¨¥É¸ œ ¨³ª·›„¸ µ¦‹—´ ®¤¼n ®µ‹Îµœªœ­¤µ„· …°ŠÂŽ¤Áž¨d ­ÁžŽÅ—o 1.3 œ´„Á¦¥¸ œ®µ‡ªµ¤œnµ‹³Ážœ} …°ŠÁ®˜»„µ¦–rŗo 2. œª‡ªµ¤‡—· ®¨´„ „žo { ®µÃ‹š¥r Á¦Éº°Š ‡ªµ¤œnµ‹³Ážœ} ‹³˜°o ŠœµÎ ‡ªµ¤¦o¼ Á¦Éº°Š ª·›¸Á¦¸¥Š­´ Áž¨¸É¥œ ¨³ª›· ¸„µ¦‹—´ ®¤¤¼n µ čÁo ¡É°º ®µ‹µÎ œªœ­¤µ·„…°ŠÂŽ¤Ážd¨­ÁžŽ ¨³‹Îµœªœ­¤µ·„…°ŠÁ®˜»„µ¦–ršµÎ Ä®Áo ®Èœ‡–» ‡nµÂ¨³˜¦³®œ„´ Ĝ„¦³ªœ„µ¦‡·—š¤¸É ¸Á®˜Ÿ» ¨ 3. Áœ°ºÊ ®µ­µ¦³ ˚¥rž{ ®µ Á¦É°º Š ‡ªµ¤œµn ‹³Ážœ} ŽŠ¹É ˜o°ŠÄo‡ªµ¤¦o¼ Á¦Éº°Š ª›· Á¸ ¦¥¸ Š­´Áž¨É¥¸ œÂ¨³ª·›¸„µ¦‹—´ ®¤¼n 4. „¦³ªœ„µ¦‹´—„µ¦Á¦¥¸ œ¦o¼ 4.1 ‡¦Â¼ œ³œÎµœ„´ Á¦¥¸ œªµn „µ¦Â„ož{ ®µÃ‹š¥r Á¦º°É Š ‡ªµ¤œµn ‹³Ážœ} œœ´Ê ­ªn œšÉ¸­Îµ‡´ ‡°º „µ¦°nµœ ˚¥r ŽÉŠ¹ œ´„Á¦¸¥œ‹³˜o°ŠÂ¥„Â¥³Ä®Åo —ªo µn ­nªœÅ®œ…°ŠÃ‹š¥r °„Á®˜„» µ¦–r ®¦°º °„ÂŽ¤Áž¨d ­ÁžŽ Ž¹ÉŠ‹³¡ªµn Á®˜„» µ¦–šr ¸ÅÉ ¤¤n ¸ÁŠÉ°º œÅ…‹³Áž}œÂŽ¤Ážd¨­ÁžŽ Á®˜»„µ¦–ršÉ¸¤Á¸ Šº°É œÅ…‹³Ážœ} Á®˜„» µ¦–r 4.2 ‡¦¥¼ „˜´ª°¥nµŠÃ‹š¥žr { ®µÁ„¥É¸ ª„´ ‡ªµ¤œµn ‹³Ážœ} 4.3 Ä®œo „´ Á¦¥¸ œšÎµÄŠµœš¸É 3 4.4 ˜¦ª‹­°‡ªµ¤™„¼ ˜°o Š…°ŠÄŠµœš¸É 3 ¨³Ážd—ð„µ­Ä®œo „´ Á¦¸¥œŽ„´ ™µ¤…°o ­Š­´¥Â¨³Ä®o œ´„Á¦¸¥œšµÎ  „f ®´—šÉ¸ 1

14 ⌫ ⌫  ⌦  ⌫      5. ®¨nŠÁ¦¥¸ œ¦o¼ 5.1 ĝŠµœšÉ¸ 3 5.2  „f ®—´ š¸É 1 6. „¦³ªœ„µ¦ª´—Ÿ¨ž¦³Á¤œ· Ÿ¨ „µ¦ª´—Ÿ¨ „µ¦ž¦³Á¤œ· Ÿ¨ 1. ­Š´ Á„˜„µ¦–¦r ªn ¤„‹· „¦¦¤…°Šœ„´ Á¦¥¸ œ 1. œ„´ Á¦¸¥œ Ťn¦ªn ¤„·‹„¦¦¤ ˜o°Šž¦´ ž¦Š» ¦nª¤„‹· „¦¦¤ —¸ 2. ˜¦ª‹­°‡ªµ¤™¼„˜o°Š…°ŠÄŠµœš¸É 3 2. œ„´ Á¦¥¸ œšÎµÅ—o 0 – 3 ˜o°Šž¦´ž¦»Š 4 – 6 —¸ 7 – 8 —¸¤µ„ 3. ตรวจสอบความถูกตองของแบบฝกหัดท่ี 1 3. œ´„Á¦¥¸ œšÎµÅ—o 0 – 2 ˜o°Šž¦´ ž¦»Š 3. ˜¦ª‹­°‡ªµ¤™„¼ ˜°o Š…°ŠÂ f„®—´ šÉ¸ 1 3 – 4 —¸ 5 – 6 —¸¤µ„ 7. œ´ š„¹ ®¨´Š­°œ ………………………………………………………………………………………………………..……… …….……...…………………………………………………………………………………………..……… ..……...……………………………………………………………………………………………….……… ………………………………………………………………………………………………………..……… ………………………………………………………………………………………………………..……… 8. „‹· „¦¦¤Á­œ°Âœ³ ………………………………………………………………………………………………………..……… …….……...…………………………………………………………………………………………..……… ..……...……………………………………………………………………………………………….……… ………………………………………………………………………………………………………..……… ………………………………………………………………………………………………………..………

⌦ 15 ⌦ ĝŠµœš¸É 3 ‡µÎ Âʸ ‹Š œ´„Á¦¥¸ œ°nµœÃ‹š¥Âr ˜¨n ³…°o ¨oªÁ˜·¤‡Îµ˜°Äœn°Šªµn Š 1. ¤­¸ ¨µ„ 14 ĝ ¤®¸ ¤µ¥Á¨…„µÎ „´ Ūoš„» ĝ ×¥¤®¸ ¤µ¥Á¨…š¸ÉÁžœ} ‹µÎ œªœª„ 7 ĝ ¤®¸ ¤µ¥Á¨…šÁ¸É žœ} ‹Îµœªœ ¨ 6 ĝ ¤®¸ ¤µ¥Á¨…«¼œ¥r 1 ĝ ™oµ­»n¤®¥·­¨µ„°°„¤µ 4 ĝ ‹Š®µ‡ªµ¤œµn ‹³Ážœ} š¸É‹³Å—o 1.1 Ÿ¨‡–¼ …°Š®¤µ¥Á¨…Äœ­¨µ„š´ÊŠ­¸É Ášµn „´ 0 ‹µ„Ëš¥…r °o œÊ¡¸ ªnµ E : „µ¦®¥· ­¨µ„ 4 ĝ Ž¹ŠÉ ¤Ÿ¸ ¨‡–¼ Áž}œ 0 ­—Šªµn ®¥· ­¨µ„šÉ¸Ážœ} 0 ¤µ®œÉŠ¹ ĝ ¨³®¥· ­¨µ„šÉ¤¸ ¸®¤µ¥Á¨…°ºœÉ Ç ¤µ°„¸ 3 ĝ S : „µ¦®¥·­¨µ„°¥nµŠÅ¦„ÅÈ —Âo ˜Än ®Åo —o 4 ĝ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 1.2 Ÿ¨‡¼–…°Š®¤µ¥Á¨…Äœ­¨µ„šÊŠ´ ­Áɸ žœ} ‹µÎ œªœª„ E : „µ¦®¥· ­¨µ„ 4 ĝ ŽÉ¹Š¤Ÿ¸ ¨‡–¼ Áž}œ‹Îµœªœª„ ­—ŠªnµÅ¤®n ¥·­¨µ„š¸ÉÁž}œ«¼œ¥r ˜˜n °o Š ®¥·™¹Š 3  ‡º° - ®¥· ‹Îµœªœª„šŠÊ´ 4 ĝ - ®¥· ‹µÎ œªœª„ 2 ĝ ¨³ ‹Îµœªœ¨ 2 ĝ - ®¥·‹µÎ œªœ¨ 4 ĝ S : „µ¦®¥· ­¨µ„°¥nµŠÅ¦„Èŗo˜Än ®Åo —o 4 ĝ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 2. ‹µ„„µ¦Ã¥œ¨¼„Á˜µq 2 ¨„¼ šÂɸ ˜„˜µn Š„œ´ ‹Š®µ‡ªµ¤œµn ‹³Ážœ} …°ŠÁ®˜„» µ¦–šr Ÿ¸É ¨¦ª¤…°ŠÂ˜¤o …°Š¨„¼ Á˜µq Ážœ} 8 E : Á®˜»„µ¦–šr Á¸É „—· …¹œÊ ‹µ„„µ¦Ã¥œ¨¼„Á˜µq ­°Š¨¼„šÉ¸Â˜„˜nµŠ„œ´ ¨ªo ŗŸo ¨¦ª¤…°Š¨¼„Á˜qµÁžœ} 8 S : Á®˜„» µ¦–šr Á¸É „·—…œ¹Ê ŗšo Ê´Š®¤—‹µ„„µ¦Ã¥œ¨„¼ Á˜qµ­°Š¨¼„šÂɸ ˜„˜µn Š„œ´ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........

16 ⌫ ⌫  ⌦  ⌫      3. Ĝ„µ¦ÂnŠŸo¼ µ¥ 5 ‡œ ¨³Ÿo®¼ ·Š 3 ‡œ Á…µo ¡´„®o°Š¡„´ 3 ®o°Š ×¥¤®¸ o°ŠÇ ®œŠÉ¹ ¡´„Å—o 2 ‡œ ­ªn œ°„¸ 2 ®°o Š ŗo¡„´ ®o°Š¨³ 3 ‡œ ‹Š®µ‡ªµ¤œnµ‹³Ážœ} …°ŠÁ®˜»„µ¦–ršÉŸ¸ ¼®o ·Š 3 ‡œ ŗo¡„´ ®o°ŠÁ—¥¸ ª„œ´ E : Á®˜»„µ¦–ršÉŸ¸ ¼®o ·Š 3 ‡œ ŗo¡„´ ®o°ŠÁ—¥¸ ª„´œ ­—Šªµn Ÿ®¼o ·ŠÁ¨°º „®o°ŠÅ—o 2 ®°o Š ¨³‹³˜°o Š Šn Ÿ¼oµ¥ 5 ‡œ Ážœ} 2 „¨»n¤Ç ¨³ 2 , 3 ‡œ S : Á®˜„» µ¦–šr ¸É榋³¡„´ ®°o ŠÄ—„ÅÈ —o ­—Šªnµ‹³˜o°ŠÂnŠ‡œ 8 ‡œ Ážœ} 3 „¨¤»n Ç ¨³ 2 , 3 ¨³ 3 ‡œ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 4. ‹µ„„µ¦Ã¥œ¨„¼ Á˜qµÁšÉ¸¥Š˜¦Š 4 ¨„¼ ¡¦o°¤„´œ 1 ‡¦´ÊŠ ‡ªµ¤œnµ‹³Ážœ} š‹¸É ³Å—Âo ˜¤o œ¨„¼ Á˜µq šŠ´Ê 4 Ážœ} ˜o¤‡n¼ 3 ¨„¼ ¨³Â˜¤o ‡¸É 1 ¨„¼ Ážœ} ÁšnµÄ— n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 5. ­¤µ¥Â¨³ž¦¸µÁ¨œn Á„¤š°—¨¼„Á˜µq …Šn „´œ ×¥š°—¨„¼ Á˜µq ‡œ¨³ 1 ¨¼„¡¦o°¤„œ´ ™oµ¨¼„Á˜qµš´ÊŠ­°Š°°„ ˜o¤‡¼n ­¤µ¥‹³Ážœ} Ÿ¼o œ³ ˜n™µo ¨„¼ Á˜qµšÊŠ´ ­°Š°°„˜o¤‡É¸ ž¦¸ µ‹³Ážœ} Ÿo¼ œ³ Ÿ¨œ°„Á®œº°‹µ„œ™¸Ê º° ªnµÁ­¤°„´œ ™µo šŠÊ´ ­°ŠÁ¨œn Á„¤œ¸Ê 20 Á„¤ ð„µ­š‹É¸ ³Á­¤°„´œ¤„¸ ‡É¸ ¦ÊŠ´ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ ĜšÉœ¸ ʸ P(E) = ................... ®¤µ¥™¹Š ‡ªµ¤œnµ‹³Ážœ} …°ŠÁ®˜»„µ¦–šr ‹É¸ ³Á­¤°„´œÄœ„µ¦Â…Šn …œ´ 1 ‡¦Ê´Š —´ŠœÊ´œ ð„µ­š¸‹É ³Á­¤°„œ´ ‹µ„„µ¦Â…nŠ…´œ 20 ‡¦Ê´Š Ážœ} ...................................... ‡¦ŠÊ´ 6. œ´„Á¦¸¥œ„¨¤n» ®œŠ¹É ‹Îµœªœ 8 ‡œ Ĝ‹µÎ œªœœÊ¸¤¸ œµ¥ „. , œµ¥ …. ¨³œµ¥ ‡. ¦ª¤°¥n—¼ ªo ¥ ™µo ­¤»n Á¨º°„ œ„´ Á¦¸¥œÁ®¨nµœ°¸Ê °„¤µ 4 ‡œ ‹Š®µ‡ªµ¤œnµ‹³Ážœ} …°ŠÁ®˜„» µ¦–r˜n°ÅžœÊ¸ 6.1 ŗošÊŠ´ œµ¥ „. , œµ¥ …. ¨³œµ¥ ‡. n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........

⌦ 17 ⌦ 6.2 ŗo œµ¥ „. , œµ¥ …. ®¦°º œµ¥ ‡. Á¡¥¸ Š 2 ‡œÁšµn œœÊ´ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 6.3 ŗo œµ¥ „. ˜Ån ¤Ån —o œµ¥ …. n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 7. Ĝ„µ¦šµÎ …°o ­° ™„¼ - Ÿ·— 10 …o° °¥µn ŠÁ—µ­n»¤ ‹Š®µ‡ªµ¤œµn ‹³Áž}œšÉœ¸ ´„Á¦¥¸ œ‡œ®œÉ¹Š‹³šÎµ…°o ­°š´ÊŠ 10 …°o ŗ˜o µ¤ÁŠºÉ°œÅ…˜°n ޜʸ 7.1 ™„¼ ˜°o Šš´ÊŠ 10 …°o n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 7.2 ™„¼ ˜o°ŠÁ¡¥¸ Š 7 …o° n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 7.3 ™„¼ ˜o°Š°¥µn Šœ°o ¥ 8 …°o n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........

18 ⌫ ⌫  ⌦  ⌫      7.4 ™„¼ ˜o°Š 50% n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........ 8. ­¨µ„„»«¨Äœ®œªn ¥ŠµœÂ®Šn ®œÉŠ¹ ¤°¸ °„‹µÎ ®œnµ¥Á¡¥¸ Š 15 ĝ ×¥¤¸ 2 ĝš‹¸É ³Å—¦o ´¦µŠª´¨ ‡º° ¦µŠª¨´ š¸É 1 ¨³¦µŠª¨´ šÉ¸ 2 ™µo œµŠ­µª¤µ¨Ž¸ º°Ê ­¨µ„ 3 ĝ ‹Š®µ‡ªµ¤œµn ‹³Ážœ} šÉÁ¸ ›°‹³Å—¦o ´¦µŠª´¨ n (E) = ………………..………………………………………….…………………….……… n (S) = ………………..……………………………………………..………………................ P (E) = ……………………………………………………………………………………........

⌦ 19 ⌦  „f ®—´ šÉ¸ 1 ‡ÎµÊ¸Â‹Š œ„´ Á¦¥¸ œÂ­—Šª›· š¸ µÎ ˚¥rž{®µ˜°n ޜʸ 1. Ĝ„µ¦‹—´ µ¥ 8 ‡œ š¤É¸ ¸ °ºÉ ŤŽn µÎÊ „´œÁ…µo ¡´„Á¦°º œ¦´¦°Š®¨Š´ ®œŠÉ¹ š¤É¸ ¸ 4 ®o°Š ™oµ¤¸ 1 ®°o Š°¥n¼Å—o 3 ‡œ ¤¸ 2 ®o°Š°¥¼nŗ®o °o Š¨³ 2 ‡œ ¨³°¸„ 1 ®°o Š °¥¼Ån —o 1 ‡œ ™µo œµ¥­¤µ¥Â¨³œµ¥­¤«„´ —Á·Í žœ} µ¥ 2 ‡œÄœ‹Îµœªœ 8 ‡œœÂ¸Ê ¨ªo ‹Š®µ‡ªµ¤œnµ‹³Áž}œšÉ­¸ ¤µ¥Â¨³­¤«„´ —Å·Í ¤¡n „´ °¥®n¼ °o ŠÁ—¥¸ ª„œ´ 2. ‹µ„œ´„Á¦¥¸ œšÊ´Š®¤— 10 ‡œ ŽÉ¹ŠÁž}œµ¥ 5 ‡œ ( ¤¸œµ¥­¤µ¥¦ª¤°¥—¼n ªo ¥ ) ¨³®Š· 5 ‡œ ‹Š®µ‡ªµ¤œµn ‹³Áž}œÄœ„µ¦Á¨º°„˜ª´ šœ…°Šœ„´ Á¦¥¸ œ„¨¤»n œ¸Ê‹µÎ œªœ 5 ‡œ ×¥Ážœ} µ¥ 3 ‡œ ®Š· 2 ‡œ ¨³œµ¥­¤µ¥‹³˜o°ŠÁžœ} ˜ª´ šœ—oª¥ 3. ¤¸Á¨… 8 ‹Îµœªœ Áž}œÁ¨…ª„ 6 ‹µÎ œªœŽŠÉ¹ Áž}œ‹Îµœªœ‡n¼ 3 ‹Îµœªœ ‹Îµœªœ‡¸É 3 ‹Îµœªœ ¨³Ážœ} Á¨…¨ 2 ‹µÎ œªœ Ž¹ŠÉ Ážœ} ‹Îµœªœ‡¼n 1 ‹µÎ œªœ ‹Îµœªœ‡É¸ 1 ‹µÎ œªœ ™oµ­¤»n Á¨…‹µÎ œªœ—´Š„¨µn ª¤µ 4 ‹µÎ œªœ ‹Š®µ‡ªµ¤œµn ‹³Áž}œšŸ¸É ¨‡–¼ …°ŠÁ¨…šŠÊ´ ­É‹¸ 圪œ¤‡¸ nµœ°o ¥„ªnµ 0 ¨³Áž}œÁ¨…‡É¸ 4. ™µo ˜o°Š„µ¦Á¨°º „„¦¦¤„µ¦ 3 ‡œ ‹µ„‡n¼­µ¤¸£¦¦¥µ 4 ‡¼n ‹Š®µ‡ªµ¤œµn ‹³Ážœ} š¸‹É ³Á¨°º „Å—o „¦¦¤„µ¦šÅ¸É ¤¤n ­¸ µ¤¸Â¨³£¦¦¥µÁž}œ„¦¦¤„µ¦¡¦o°¤„´œ 5. „¨n°ŠÄ®œŠÉ¹ ¦¦‹ž» µ„„µ 1 î¨ Áž}œžµ„„µÂ—Š 3 —µo ¤ ­Á¸ …¸¥ª 4 —µo ¤ š¸ÁÉ ®¨º°Áž}œ­œ¸ ÎʵÁŠ·œ ‹Š®µ‡ªµ¤œµn ‹³Áž}œš¸É­»¤n ®¥· žµ„„µ¤µ 3 —µo ¤Â¨oªÅ—o‡¦š„» ­¸ 6. „¨°n ŠÄ®œÉ¹Š¤¸¨„¼ „ªo …œµ—Á—¥¸ ª„´œ 13 ¨„¼ Ážœ} ­Â¸ —Š 6 ¨„¼ ­…¸ µª 4 ¨¼„ œ°„œœ´Ê Ážœ} ­Á¸ ®¨º°Š ­»n¤®¥·¨„¼ „ªo ¤µ 2 ¨„¼ ‹Š®µ‡ªµ¤œnµ‹³Áž}œš¸É‹³Å—¨o ¼„„ªo ˜µn Š­„¸ ´œ

20 ⌫ ⌫  ⌦  ⌫      Ÿœ„µ¦‹´—„µ¦Á¦¸¥œ¦¼ošÉ¸ 4 Á¦É°º Š ¥Á¼ œ¸¥œ °·œÁ˜°¦rÁŽ„´œ ‡°¤¡¨¸Á¤œ˜r ¨³Á®˜„» µ¦–rš¸ÅÉ ¤nÁ„·—¦nª¤„œ´ Êœ´ ¤´›¥¤«„¹ ¬µžše ɸ 6 ª· µ ‡–·˜«µ­˜¦r Áª¨µ 3 ª´É äŠ Ÿ¨„µ¦Á¦¸¥œ¦šo¼ ¸‡É µ—®ªŠ´ œ„´ Á¦¥¸ œ­µ¤µ¦™®µ‡ªµ¤œµn ‹³Áž}œ…°ŠÁ®˜»„µ¦–Žr ¹ÉŠÁ„—· ‹µ„„µ¦¥¼Áœ¥¸ œ °œ· Á˜°¦rÁŽ„´œ ‡°¤¡¨¸Á¤œ˜r ®¦º° Ÿ¨˜µn Š¦³®ªnµŠÁŽ˜Å—o 1. ‹—» ž¦³­Š‡r„µ¦Á¦¸¥œ¦o¼ 1.1 œ´„Á¦¥¸ œ­µ¤µ¦™®µ‹Îµœªœ­¤µ„· …°ŠÁ®˜»„µ¦–År —o 1.2 œ„´ Á¦¥¸ œ®µ‹µÎ œªœ­¤µ·„…°ŠÂŽ¤Ážd¨­ÁžŽÅ—o 1.3 œ„´ Á¦¸¥œ®µ‡ªµ¤œnµ‹³Ážœ} …°ŠÁ®˜„» µ¦–rŗo 2. œª‡ªµ¤‡—· ®¨„´ „µ¦«„¹ ¬µ Á¦Éº°Š ¥¼Áœ¥¸ œ °·œÁ˜°¦Ár Ž„´œ ‡°¤¡¨Á¸ ¤œ˜r ¨³Á®˜„» µ¦–šr ÉŸ ¤nÁ„—· ¦nª¤„œ´ šÎµÄ®¤o ¸ ‡ªµ¤¦‡o¼ ªµ¤Á…µo ċ ­µ¤µ¦™®µ‡ªµ¤œnµ‹³Ážœ} …°ŠÁ®˜„» µ¦–r®¨µ¥Ç Á®˜„» µ¦–r š—¸É µÎ Áœœ· „µ¦£µ¥Ä˜o˜ª´ —εÁœ·œ„µ¦…°ŠÁŽ˜Å—o°¥µn Š™„¼ ˜°o Š ¨³˜¦³®œ„´ ™Š¹ ‡–» ‡µn …°Š„µ¦ÁÉº°¤Ã¥Š‡ªµ¤¦š¼o Áɸ „¥¸É ª…o°Š„œ´ 3. ÁœºÊ°®µ­µ¦³ ™oµ E1 ¨³ E2 Ážœ} Á®˜»„µ¦–Är —Ç Ž¹ÉŠÁžœ} ­´ ÁŽ˜…°ŠÂŽ¤Áž¨d ­ÁžŽ S ¨ªo 3.1 nE1 ‰ E2 nE1  nE2  nE1 ˆ E2 3.2 E1 ˆ E2 I „Șn°Á¤°ºÉ E1 ¨³ E2 Ážœ} Á®˜„» µ¦–ršÅ¸É ¤Án „—· ¦nª¤„´œ 3.3 E1c S  E1 4. „¦³ªœ„µ¦‹´—„µ¦Á¦¥¸ œ¦o¼ 4.1 ‡¦š¼ šªœ‡ªµ¤¦¼o Á¦Éº°Š ÁŽ˜ ץĮoœ„´ Á¦¸¥œ˜°‡µÎ ™µ¤ÄœÄŠµœšÉ¸ 4 4.2 œ„´ Á¦¸¥œšµÎ  „f ®´—šÉ¸ 2 ץĮoœ´„Á¦¸¥œ­µ¤µ¦™ž¦„¹ ¬µ¡—¼ ‡¥» ™µ¤Á¡Éº°œ®¦°º ‡¦„¼ ÅÈ —o 4.3 œ´„Á¦¸¥œÂ¨³‡¦¼ªn ¥„œ´ ­¦»ž®¨Š´ ‹µ„šÉŸ —o˜¦ª‹­°‡ªµ¤™„¼ ˜o°Š…°ŠÂ f„®—´ šÉ¸ 2 ŗªo µn ™oµ A ¨³ B Ážœ} Á®˜»„µ¦–Är —Ç ĜŽ¤Áž¨d ­ÁžŽ S ¨ªo 4.3.1 nA ‰ B nA  nB  nA ˆ B 4.3.2 nA ˆ B nA  nB  nA ‰ B

⌦ 21 ⌦ 4.3.3 nA B nA ˆ Bc nA  nA ˆ B 4.3.4 nB  A nB ˆ Ac nB  nB ˆ A 4.3.5 A ˆ B I „˜È °n Á¤°ºÉ A ¨³ B Ážœ} Á®˜„» µ¦–šr Åɸ ¤nÁ„·—¦ªn ¤„œ´ 4.3.6 ™oµ A , B ¨³ C Áž}œÁ®˜»„µ¦–Är —Ç ĜŽ¤Áž¨d ­ÁžŽ S ¨oª nA‰ B ‰C nA  nB nC  nAˆ B  nAˆC  nB ˆC  nAˆ B ˆC 4.3.7 ™oµ A Áž}œÁ®˜„» µ¦–rÄ—Ç ÄœÂŽ¤Ážd¨­ÁžŽ S ¨oª nAc nU  nA 5. ®¨Šn Á¦¸¥œ¦¼o 5.1 ĝŠµœš¸É 4 5.2  f„®—´ šÉ¸ 2 6. „¦³ªœ„µ¦ª´—Ÿ¨ž¦³Á¤œ· Ÿ¨ „µ¦ž¦³Á¤œ· Ÿ¨ „µ¦ª—´ Ÿ¨ 1. œ´„Á¦¸¥œ Ť¦n nª¤„‹· „¦¦¤ ˜°o Šž¦´ž¦»Š 1. ­´ŠÁ„˜„µ¦–¦r nª¤„‹· „¦¦¤…°Šœ´„Á¦¥¸ œ ¦ªn ¤„·‹„¦¦¤ —¸ 2. ˜¦ª‹­°‡ªµ¤™¼„˜°o Š…°ŠÄŠµœš¸É 4 2. œ´„Á¦¥¸ œšÎµÅ—o 0 – 4 …°o ˜o°Šž¦´ ž¦»Š 3. ˜¦ª‹­°‡ªµ¤™¼„˜°o Š…°ŠÂ f„®—´ š¸É 2 5 – 8 …o° —¸ 9 – 10 …°o —¤¸ µ„ 3. œ´„Á¦¥¸ œšµÎ ŗo 0 – 3 …o° ˜°o Šž¦´ ž¦»Š 3 – 5 …o° —¸ 6 …°o —¸¤µ„ 7. ´œš„¹ ®¨Š´ ­°œ ……………………………………………………………………………………………………………… ……….…...………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… 8. „·‹„¦¦¤Á­œ°Âœ³ ……………………………………………………………………………………………………………… ……….…...………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ………………………………………………………………………………………………………………

22 ⌫ ⌫  ⌦  ⌫      ĝŠµœš¸É 4 ‡ÎµÂʸ ‹Š ‹µ„Ÿœ£µ¡Áªœœr…µo Š¨µn ŠœÊ¸ ™oµ S Áž}œÂŽ¤Áž¨d ­ÁžŽ ¨³ E1 ¨³ E2 Ážœ} Á®˜»„µ¦–r ŽŠ¹É E1  S ¨³ E2  S „ε®œ—Ä®o nE1 n1 , nE2 n2 ¨³ nE1 ˆ E2 n3 Ä®o œ´„Á¦¥¸ œÁ˜¤· ‡µÎ ˜°¨ŠÄœ°n ŠªnµŠ˜°n ޜʸ E1 E2 E1  E2 E2  E1 E1 ˆ E2 1. E1 ‰ E2 = ..................................................................................................................................... 2. E1 ˆ E2 = ..................................................................................................................................... 3. E1  E2 = ..................................................................................................................................... 4. E2  E1 = ..................................................................................................................................... = ..................................................................................................................................... 5. E1c = ..................................................................................................................................... = ..................................................................................................................................... 6. E c 2 7. E1 ˆ E c 2 8. nE1 ‰ E2 = ..................................................................................................................................... 9. nE1  E2 = ..................................................................................................................................... 10. nE2  E1 = .....................................................................................................................................

⌦ 23 ⌦  „f ®—´ š¸É 2 ‡ÎµÊ¸Â‹Š œ„´ Á¦¥¸ œÁ˜¤· ‡µÎ ˜°Äœ°n ŠªnµŠ 1. Ã¥œ¨„¼ Á˜qµ 2 ¨„¼ 1 ‡¦ÊŠ´ Ÿ¨¨´¡›šr ­¸É œÄ‹‡º°Â˜o¤šÉ¸‹³Á„—· …Êœ¹ „µÎ ®œ—Ä®o S : ÁŽ˜…°ŠÂŽ¤Ážd¨­ÁžŽ A : šœÁŽ˜…°ŠÁ®˜„» µ¦–šr ɟ¸ ¨ª„…°ŠÂ˜¤o Áž}œ 6 B : šœÁŽ˜…°ŠÁ®˜»„µ¦–šr Â¸É ˜o¤…°Š¨¼„Á˜µq Áž}œ‹Îµœªœ‡šn¼ Ê´Š­°Š¨¼„ C : šœÁŽ˜…°ŠÁ®˜»„µ¦–šr Âɸ ˜o¤…°Š¨„¼ Á˜µq Áž}œ‹µÎ œªœ‡¸šÉ ʊ´ ­°Š¨¼„ D : šœÁŽ˜…°ŠÁ®˜„» µ¦–šr ¸ÉŸ¨ª„…°ŠÂ˜o¤Ážœ} 8 ‹ŠÁ…¥¸ œÁžœ} ÁŽ˜…°Š‡¼°n œ´ —´ ×¥­¤µ„· ˜ª´ ®œµo Ážœ} ˜o¤…°Š¨„¼ Á˜µq ¨„¼ šÉ¸ 1 ­¤µ„· ˜ª´ ®¨´ŠÁžœ} ˜¤o …°Š ¨¼„Á˜µq ¨„¼ šÉ¸ 2 A = .......................................................................................................................................... B = .......................................................................................................................................... C = .......................................................................................................................................... D = .......................................................................................................................................... A ‰ B = ......................................................................................................................................... A ‰ C = ......................................................................................................................................... A ˆ C = ......................................................................................................................................... A ˆ B = ......................................................................................................................................... C ˆ B = ......................................................................................................................................... A ˆ Bc = ......................................................................................................................................... 2. Ã¥œÁ®¦¥¸  3 Á®¦¸¥ 1 ‡¦Š´Ê ­œÄ‹®œoµ…°ŠÁ®¦¥¸ šÊŠ´ ­µ¤š¸ÉÁ„—· …¹œÊ „ε®œ—Ä®o S : ÁŽ˜…°ŠÂŽ¤Áž¨d ­ÁžŽ A : šœÁŽ˜…°ŠÁ®˜»„µ¦–šr ¸ÉÁ®¦¸¥…ʹœ®œoµÁ®¤º°œ„´œšÊ´Š­µ¤Á®¦¸¥ B : šœÁŽ˜…°ŠÁ®˜»„µ¦–šr ¸…É œÊ¹ „°o ¥°¥µn Šœ°o ¥ 2 Á®¦¥¸  C : šœÁŽ˜…°ŠÁ®˜„» µ¦–šr ¸É…¹Êœ®´ª¤µ„„ªnµ„°o ¥ ‹Š®µ ( čo H šœ „µ¦…œÊ¹ ®ª´ 1 ‡¦Š´Ê čo T šœ „µ¦…œ¹Ê „o°¥ 1 ‡¦´ÊŠ ) A = ......................................................................................................................................... B = ..........................................................................................................................................

24 ⌫ ⌫  ⌦  ⌫      C = ......................................................................................................................................... A ‰ B = ......................................................................................................................................... A ‰ C = ......................................................................................................................................... B ˆ C = ......................................................................................................................................... A – B = .......................................................................................................................................... Ac = ......................................................................................................................................... 3. ‹µ„„µ¦­Îµ¦ª‹­»…£µ¡œ„´ Á¦¥¸ œŽÉ¹Š¤¸ 40 ‡œ ¡ªµn ¤œ¸ ´„Á¦¥¸ œ­µ¥˜µ­Êœ´ 15 ‡œ ¤¸œ´„Á¦¸¥œš¸ÁÉ ž}œ 懢{œ 20 ‡œ ¨³œ´„Á¦¥¸ œšÉ¸Áž}œš´ÊŠÃ¦‡¢{œÂ¨³­µ¥˜µ­´Êœ 4 ‡œ ‹Š®µ‹Îµœªœœ„´ Á¦¥¸ œšÉ¸Áž}œÃ¦‡¢{œ ®¦°º ­µ¥˜µ­Êœ´ .............................................................................................. 4. Ĝ„µ¦­µÎ ¦ª‹„µ¦¨Šš³Á¸¥œª· µ‡–˜· «µ­˜¦r ¢d­„· ­r ¨³£µ¬µ°Š´ „§¬…°Šœ„´ Á¦¥¸ œÃ¦ŠÁ¦¥¸ œÂ®nŠ ®œ¹ÉŠ‹µÎ œªœ 100 ‡œ ¤œ¸ „´ Á¦¸¥œ¨Šš³Á¥¸ œš´ÊŠ 3 ª·µ ‹µÎ œªœ 26 ‡œ ¤¸ŸÁo¼ ¦¥¸ œª· µ‡–˜· «µ­˜¦r¨³ ¢d­„· ­r ‹Îµœªœ 39 ‡œ ¤¸Ÿ¼Áo ¦¸¥œª· µ¢­d „· ­r¨³£µ¬µ°´Š„§¬ ˜Ån ¤Án ¦¥¸ œª·µ‡–˜· «µ­˜¦r ‹µÎ œªœ 15 ‡œ ¤¸ŸoÁ¼ ¦¥¸ œ 2 ª· µ ‹µ„ 3 ª· µ ‹µÎ œªœ 45 ‡œ ¤Ÿ¸ o¼Á¦¥¸ œª· µ£µ¬µ°Š´ „§¬ ‹µÎ œªœ 60 ‡œ ¢­d ·„­r ‹Îµœªœ 59 ‡œ ¨³Á¦¸¥œÁ¡¥¸ Šª· µÁ—¥¸ ª 10 ‡œ ‹Š®µ‹µÎ œªœœ´„Á¦¥¸ œš¸ÁÉ ¦¥¸ œ°¥nµŠœ°o ¥ 1 ª·µ ‹µ„ 3 ª· µœ¸Ê ....................................................................... 5. Ĝ„µ¦­Îµ¦ª‹œ„´ Á¦¸¥œÊ´œž¦³™¤«¹„¬µ ‹µÎ œªœ 100 ‡œ Áž}œµ¥ 60 ‡œ Áž}œ®Š· 40 ‡œ ¡ªnµ¤¸ œ„´ Á¦¸¥œ 30 ‡œ ¢œ{ Ÿ» œ„´ Á¦¸¥œ 20 ‡œ ­µ¥˜µ­œ´Ê œ„´ Á¦¸¥œµ¥ 8 ‡œ ¢œ{ Ÿ» œ„´ Á¦¥¸ œ 3 ‡œ ¢œ{ ŸÂ» ¨³ ­µ¥˜µ­Êœ´ œ„´ Á¦¸¥œ 12 ‡œ ­µ¥˜µ­Ê´œ œ„´ Á¦¸¥œ®·Š 3 ‡œ ¢{œŸÂ» ¨³­µ¥˜µ­Ê´œ ‹Š®µ‹µÎ œªœœ„´ Á¦¸¥œ š¸É¢œ{ ŤŸn »Â¨³­µ¥˜µÅ¤­n œÊ´ .............................................................................................

⌦ 25 ⌦ Ÿœ„µ¦‹´—„µ¦Á¦¸¥œ¦o¼šÉ¸ 5 Á¦°Éº Š ‡ªµ¤œnµ‹³Ážœ} ץč‡o ªµ¤¦¼o Á¦°Éº Š ¥Á¼ œ¥¸ œ °·œÁ˜°¦rÁŽ„œ´ ‡°¤¡¨Á¸ ¤œ˜r ´Êœ¤›´ ¥¤«„¹ ¬µžše ɸ 6 ª· µ ‡–·˜«µ­˜¦r Áª¨µ 3 Éª´ äŠ Ÿ¨„µ¦Á¦¥¸ œ¦šo¼ ɇ¸ µ—®ªŠ´ œœ„´ Á´„¦Á¥¸¦œ¸¥œ­­µ¤µ¤µ¦µ™¦®™®µ‡µµn‡‡nµª‡µª¤µ¤œœnµ‹µn ³‹Á³žÁžœ} œ}…°…Š°ÁŠ®Á®˜„»˜µ„» ¦µ–¦–År —År o—o 1. ‹—» ž¦³­Š‡„r µ¦Á¦¥¸ œ¦¼o œ´„Á¦¥¸ œ¤‡¸ ªµ¤­µ¤µ¦™®µ‡ªµ¤œµn ‹³Ážœ} …°ŠÁ®˜»„µ¦–rŗo 2. œª‡ªµ¤‡—· ®¨„´ ‡ªµ¤œnµ‹³Ážœ} …°ŠÁ®˜„» µ¦–®r ¨µ¥Ç Á®˜„» µ¦–r ­µ¤µ¦™®µÅ—Ão —¥°µ«´¥˜ª´ —εÁœ·œ„µ¦…°ŠÁŽ˜ Áœn ¥Á¼ œ¸¥œ °œ· Á˜°¦rÁŽ„œ´ ‡°¤¡¨Á¸ ¤œ˜r Ž¹ÉŠšµÎ Ä®o¤‡¸ ªµ¤¦o‡¼ ªµ¤Á…µo ċĜ„µ¦‡µÎ œª–°¥nµŠ¤Á¸ ®˜Ÿ» ¨ —´ Á‹œ 3. Áœ°ºÊ ®µ­µ¦³ ™oµ N Ážœ} ‹µÎ œªœ­¤µ·„…°ŠÂŽ¤Ážd¨­ÁžŽ S ŽŠÉ¹ ž¦³„°—oª¥‹µÎ œªœ­¤µ·„š¸¤É ¸Ã°„µ­Á„—· …ʹœÅ—o Ášµn Ç „´œ ¨³ n Ážœ} ‹µÎ œªœ­¤µ„· …°ŠÁ®˜„» µ¦–r E ŽÉ¹ŠÁž}œ­´ÁŽ˜…°Š S ¨ªo ‡ªµ¤œµn ‹³Áž}œ…°Š Á®˜»„µ¦–r E Ášµn „´ n N 4. „¦³ªœ„µ¦‹´—„µ¦Á¦¥¸ œ¦o¼ 4.1 ‡¦š¼ šªœ‡ªµ¤¦„o¼ µ¦®µ‡nµ‡ªµ¤œnµ‹³Áž}œ Ž¹ŠÉ ¤‡¸ µn Ášnµ„´ °´˜¦µ­ªn œ¦³®ªnµŠ‹µÎ œªœ­¤µ„· …°Š Á®˜„» µ¦–r ˜n°‹Îµœªœ­¤µ·„…°ŠÂŽ¤Áž¨d ­ÁžŽ 4.2 œ´„Á¦¥¸ œšµÎ ĝŠµœšÉ¸ 5 ×¥šÉœ¸ „´ Á¦¸¥œ­µ¤µ¦™ž¦„¹ ¬µ ¡—¼ ‡¥» ™µ¤Á¡º°É œ®¦º°‡¦„¼ ÅÈ —o 4.3 œ´„Á¦¥¸ œÂ¨³‡¦¼nª¥„œ´ ­¦»ž®¨Š´ ‹µ„šÉŸ —˜o ¦ª‹­°‡ªµ¤™„¼ ˜°o Š…°ŠÄŠµœš¸É 5 ªµn ™oµ A ¨³ B Ážœ} Á®˜»„µ¦–rÄ—Ç ÄœÂŽ¤Ážd¨­ÁžŽ S ¨oª 4.3.1 PA ‰ B PA  PB  PA ˆ B ®¦°º PA ˆ B PA  PB  PA ‰ B 4.3.2 PA B PA ˆ Bc PA  PA ˆ B 4.3.3 PB  A PB ˆ Ac PB  PB ˆ A 4.3.4 PA ˆ B 0 „Șn°Á¤°Éº A ¨³ B Áž}œÁ®˜„» µ¦–šr ¸ÉŤÁn „—· ¦ªn ¤„œ´

26 ⌫ ⌫  ⌦  ⌫     

⌦ 27 ⌦ ĝŠµœšÉ¸ 5 ‡Îµ¸ÂÊ ‹Š Ä®œo ´„Á¦¥¸ œÁ˜·¤‡µÎ ˜°¨ŠÄœn°Šªµn Š ™oµ S Áž}œÂŽ¤Ážd¨­ÁžŽ ¨³ E1 ¨³ E2 Ážœ} Á®˜„» µ¦–r ŽÉ¹Š E1  S ¨³ E2  S „ε®œ—Ä®o n3 , nE1 ‰ E2 n4 , nS N , nE1 n1 , nE2 n2 , nE1 ˆ E2 nE1  E2 n5 ¨³ n¨©§ E1c ¸¹· n6 ‹ŠÁ˜¤· ‡Îµ˜°Á¡°Éº ˜°‡Îµ™µ¤…°o 1 – 3 E1 E2 E1  E2 E2  E1 E1 ˆ E2 1. ‹µ„‡ªµ¤¦oÁ¼ ¦°ºÉ Š ÁŽ˜ ¡ªµn nE1 ‰ E2 nE1  nE2  nE1 ˆE 2 n4 = n1 + n2 - n3 ™oµ n4 n1  n2  n3 ®µ¦—oª¥ N šÊŠ´ šµŠŽoµ¥Â¨³šµŠ…ªµ ‹³Å—ªo µn N NN N œÉœ´ ‡º° PE1 ‰ E2 PE1  PE2  PE1 ˆ E2 2. ĜšÎµœ°ŠÁ—¸¥ª„œ´ ‹³¡ªµn nE1 ˆ E2 nE1  nE2  nE1 ‰E 2 ..................... = .................................................................... ..................... = .................................................................... ­¦»žÅ—ªo µn PE1  E2 PE1  PE1 ˆ E2 3. ĜšµÎ œ°ŠÁ—¸¥ª„´œ ‹³¡ªµn nE1  E2 ....................nE1  nE1 ˆE 2 ..................... = .................................................................... ..................... = .................................................................... ­¦»žÅ—ªo µn PE1 ˆ E2 PE1  PE2  PE1 ‰ E2

28 ⌫ ⌫  ⌦  ⌫      4. ĜšÎµœ°ŠÁ—¸¥ª„´œ ‹³¡ªnµ nE1 c .................. nS  nE1 ........................... ..................... = .................................................................... ..................... = .................................................................... ­¦ž» ŗoªµn P¨©§ E1c ·¹¸ 1  PE1 ....................... 5. ‹µ„Ÿœ£µ¡‹³­¦ž» ĜŠn…°Š‡ªµ¤œnµ‹³Ážœ} ŗ°o ¥µn ŠÅ¦ S E1 E2 Á®˜„» µ¦–r E1 ¨Á®˜„» µ¦–r E2 Áž}œ°¥µn ŠÅ¦ .................................................................................. nE1 ˆ E2 = ............................................................................................................................. nI = ............................................................................................................................................. œœÉ´ ‡º° PE1 ˆ E2 = ............................................................................................................. PI = ................................................................................................................................................ 6. ®¤n¼µo œÂ®nŠ®œ¹ÉŠ¤¸ž¦³µ„¦°µ«´¥°¥¼n 200 ‡¦°‡¦´ª ¤¸‡¦°‡¦´ªš¸Éž¨„¼ …oµª 100 ‡¦°‡¦ª´ ž¨¼„ …oµªÃ¡— 120 ‡¦°‡¦´ª ¨³ž¨¼„šÊŠ´ …µo ªÃ¡—¨³…oµª 40 ‡¦°‡¦ª´ ‹Š®µ‡ªµ¤œµn ‹³Áž}œš¸‡É ¦°‡¦ª´ œœÊ´ ‹³ž¨„¼ …oµª®¦°º …µo ªÃ¡— ‹³Å—ªo µn ™oµÄ®o A Áž}œÁŽ˜…°Š‡¦°‡¦´ªš¸žÉ ¨¼„…oµª B Áž}œÁŽ˜…°Š‡¦°‡¦´ªš¸Éž¨„¼ …µo ªÃ¡— œÉ´œ‡º° nA = ................................................. , nB = ................................................. nU = ................................................. , nA ‰ B = ........................................ PA ‰ B = ‹Îµœªœ­¤µ·„š°É¸ ¥¼Än œ A ®¦º° B = ................................................. ‹Îµœªœ­¤µ·„š¸É°¥¼nĜ U

⌦ 29 ⌦  „f ®—´ šÉ¸ 3 ‡ÎµÊ¸Â‹Š œ´„Á¦¥¸ œÂ­—Šª·›š¸ εÁ¡Éº°®µ‡µÎ ˜°…°ŠÃ‹š¥˜r °n Şœ¸Ê 11.. จ‹าµก„ก„าµร¦ส­ำεร¦วªจ‹ส­ขุ …» ภ£าµพ¡ข…อ°งŠนœกั ´„เรÁ¦ยี ¸¥นœซŽงึ่ มɊ¹ ¤ี 4¸ 040คน‡œพบ¡วา ªมµnนี ¤กั ¸œเร„´ ยี Áน¦¥¸ สœา­ยตµ¥าส˜นั้µ­1´Êœ5 1ค5น‡มœนี กั ¤เร¸œยี „´ นÁ¦ท¸¥เ่ี ปœนšโ¸ÁÉ žร}œคฟæน ‡ ¢20œ{ ค2น0 ‡แœละÂน¨ัก³œเร´„ียÁน¦ท¥¸ œ่ีเปšน¸ÉÁžทœ} ั้งโšร´ÊŠคÃฟ¦‡น¢แ{œลÂะส¨³าย­ตµา¥ส˜้ันµ­4œ´Ê ค4น‡œถา™สµo ุม­เ»n¤ลÁือ¨ก°º น„ักœเ´„รÁีย¦น¥¸ มœา¤หµน®ึ่งœคŠ¹É น‡œ จ‹งŠห®าµค‡วªาµม¤ œนnµา จ‹ะ³เÁปžนœ} ทšจี่ ɸ‹ะ³ไÅด—น œo กั „´ เรÁ¦ยี ¥¸นœทšเี่ ป¸ÁÉ žน œ}โรÃค¦ฟ‡¢น œ{หร®อื ¦โ°º รÃค¦ส‡า­ยµต¥า˜สµน้ั ­´Êœ 2. Ĝ„µ¦­Îµ¦ª‹„µ¦¨Šš³Á¸¥œª·µ‡–·˜«µ­˜¦r ¢d­·„­r ¨³£µ¬µ°´Š„§¬…°Šœ„´ Á¦¸¥œÃ¦ŠÁ¦¥¸ œÂ®nŠ®œÉŠ¹ ‹Îµœªœ 100 ‡œ ¤¸œ´„Á¦¥¸ œ¨Šš³Á¸¥œšÊ´Š 3 ª·µ ‹Îµœªœ 26 ‡œ ¤Ÿ¸ oÁ¼ ¦¸¥œª· µ‡–·˜«µ­˜¦Âr ¨³¢d­„· ­r ‹Îµœªœ 39 ‡œ ¤¸Ÿ¼Áo ¦¸¥œª·µ¢d­·„­Âr ¨³£µ¬µ°Š´ „§¬ ˜nŤnÁ¦¥¸ œª·µ‡–˜· «µ­˜¦r ‹Îµœªœ 15 ‡œ ¤¸ŸoÁ¼ ¦¸¥œ 2 ª·µ ‹µ„ 3 ª·µ ‹µÎ œªœ 45 ‡œ ¤¸ŸÁ¼o ¦¥¸ œª·µ£µ¬µ°´Š„§¬ ‹µÎ œªœ 60 ‡œ ¢d­„· ­r ‹Îµœªœ 59 ‡œ ¨³ Á¦¥¸ œÁ¡¥¸ Šª·µÁ—¥¸ ª 10 ‡œ ‹Š®µ‹µÎ œªœœ„´ Á¦¥¸ œšÁɸ ¦¥¸ œ°¥µn Šœ°o ¥ 1 ª· µ ‹µ„ 3 ª·µœÊ¸ 3. ‡¦°‡¦ª´ …°ŠŒœ´ ŞÁš¸É¥ªÁ¸¥ŠÄ®¤n Œœ´ ŗ‹o —œ´ š¹„­£µ¡°µ„µ«Åª—o ´ŠœÊ¸ µŠª´œ œ˜„ ª´œš ¸É œÅ¤˜n „ ‹³¤¸°µ„µ«Ä­˜¨°—ª´œ ™oµ œ˜„˜°œÁµo °µ„µ«˜°œµn ¥‹³Â‹¤n Ä­ ™µo  œ˜„˜°œµn ¥°µ„µ«˜°œÁoµ‹³ ‹¤n Ä­ ¦³®ªnµŠÁª¨µ¡„´ °¥¤¼n  ¸ œ˜„ 13 ªœ´ °µ„µ«Â‹¤n ĭĜ˜°œÁµo 15 ªœ´ °µ„µ«Â‹¤n ĭĜ˜°œnµ¥ 12 ª´œ ‹Š®µ‡ªµ¤œnµ‹³Ážœ} šÉ ¸ œÅ¤n˜„ 4. Ĝ„µ¦­µÎ ¦ª‹œ„´ Á¦¸¥œœÊ´ ž¦³™¤«„¹ ¬µ ‹Îµœªœ 100 ‡œ Ážœ} µ¥ 60 ‡œ Áž}œ®·Š 40 ‡œ ¡ªnµ¤¸ œ´„Á¦¸¥œ 30 ‡œ ¢œ{ Ÿ» œ„´ Á¦¥¸ œ 20 ‡œ ­µ¥˜µ­Êœ´ œ„´ Á¦¥¸ œµ¥ 8 ‡œ ¢œ{ Ÿ» œ„´ Á¦¸¥œ 3 ‡œ ¢{œŸÂ» ¨³­µ¥˜µ­´Êœ œ´„Á¦¸¥œ 12 ‡œ ­µ¥˜µ­œÊ´ œ´„Á¦¸¥œ®Š· 3 ‡œ ¢{œŸ»Â¨³­µ¥˜µ­œÊ´ ‹Š®µ‹Îµœªœœ´„Á¦¥¸ œšÉ¢¸ {œÅ¤nŸ»Â¨³ ­µ¥˜µÅ¤­n ´Êœ

30 ⌫ ⌫  ⌦  ⌫      Ÿœ„µ¦‹´—„µ¦Á¦¥¸ œ¦¼ošÉ¸ 6 Á¦ºÉ°Š „‘š­¸É µÎ ‡´µŠž¦³„µ¦Á„¸¥É ª„´ ‡ªµ¤œµn ‹³Áž}œ ´œÊ ¤´›¥¤«¹„¬µžešÉ¸ 6 ª· µ ‡–˜· «µ­˜¦r Áª¨µ 3 Éª´ äŠ Ÿ¨„µ¦Á¦¥¸ œ¦šo¼ ‡¸É µ—®ª´Š œ´„Á¦¥¸ œ­µ¤µ¦™®µ‡ªµ¤œnµ‹³Ážœ} …°ŠÁ®˜„» µ¦–rץč„o ‘š­É¸ µÎ ‡´µŠž¦³„µ¦Á„¥¸É ª„´‡ªµ¤œµn ‹³Ážœ} 1. ‹»—ž¦³­Š‡„r µ¦Á¦¥¸ œ¦o¼ 1.1 ®µ‹µÎ œªœ­¤µ„· …°ŠÁ®˜»„µ¦–År —o 1.2 ®µ‹Îµœªœ­¤µ„· …°ŠÂŽ¤Ážd¨­ÁžŽÅ—o 1.3 ®µ‡ªµ¤œµn ‹³Áž}œ…°ŠÁ®˜„» µ¦–rŗo 2. œª‡ªµ¤‡—· ®¨„´ „µ¦«¹„¬µ Á¦Éº°Š „‘šÉ­¸ 凐´ µŠž¦³„µ¦Á„¥É¸ ª„´‡ªµ¤œnµ‹³Ážœ} šµÎ Ä®¤o ‡¸ ªµ¤¦¼o ‡ªµ¤Á…µo ċÁ„¥¸É ª„´ ‡ªµ¤œµn ‹³Ážœ} …°ŠÁ®˜„» µ¦–r®¨µ¥Ç Á®˜„» µ¦–r š—ɸ εÁœœ· „µ¦£µ¥Ä˜˜o ª´ —εÁœ·œ„µ¦…°ŠÁŽ˜ šµÎ Ä®o­µ¤µ¦™ ‡µÎ œª–®µ‡ªµ¤œµn ‹³Ážœ} …°ŠÁ®˜»„µ¦–šr Áɸ „—· …Êœ¹ ŗ°o ¥nµŠ™„¼ ˜o°Š ¨³˜¦³®œ´„™Š¹ ‡–» ‡nµ„µ¦‡·—°¥µn Š¤¸ Á®˜Ÿ» ¨ 3. ÁœÊ°º ®µ­µ¦³ 3.1 „‘…o°š¸É 1 ™µo E1 ¨³ E2 Ážœ} Á®˜„» µ¦–Är —Ç ŽÉŠ¹ Ážœ} ­´ ÁŽ˜…°ŠÂŽ¤Áž¨d ­ÁžŽ S ¨ªo 3.2 „‘…°o š¸É 2 PE1 ‰ E2 PE1  PE2  PE1 ˆ E2 3.3 „‘…o°š¸É 3 ™µo E1 ¨³ E2 Ážœ} Á®˜„» µ¦–Är —Ç ŽŠ¹É Ážœ} ­´ÁŽ˜…°ŠÂŽ¤Áž¨d ­ÁžŽ S ¨oª E1 ˆ E2 I ¨ªo PE1 ‰ E2 PE1  PE2 ™µo E1 Ážœ} Á®˜»„µ¦–Är —Ç ŽŠ¹É Áž}œ­´ÁŽ˜…°ŠÂŽ¤Áž¨d ­ÁžŽ S ¨oª P§©¨ E1c ¸·¹ 1  PE1 4. „¦³ªœ„µ¦‹—´ „µ¦Á¦¥¸ œ¦¼o 4.1 ‡¦Ä¼ ®œo ´„Á¦¸¥œªn ¥„œ´ ­¦»ž­¤´˜·µŠž¦³„µ¦…°Š‡ªµ¤œµn ‹³Ážœ} ˜°n ޜʸ ™oµ A ¨³ B Áž}œÁ®˜„» µ¦–Är —Ç ĜŽ¤Áž¨d ­ÁžŽ S ¨ªo 4.1.1 PA ‰ B PA  PB  PA ˆ B ®¦°º PA ˆ B PA  PB  PA ‰ B

⌦ 31 ⌦

32 ⌫ ⌫  ⌦  ⌫      ĝŠµœšÉ¸ 6 ‡µÎ Ê¸ ‹Š œ„´ Á¦¥¸ œ«„¹ ¬µ Á¦ºÉ°Š „‘š­¸É µÎ ‡´µŠž¦³„µ¦…°Š‡ªµ¤œnµ‹³Áž}œ…°ŠÁ®˜„» µ¦–˜r °n ŞœÂʸ ¨ªo Á˜·¤ ‡µÎ ˜°¨ŠÄœn°ŠªnµŠ ™oµ A ¨³ B Áž}œÁ®˜„» µ¦–rÄ—Ç ÄœÂŽ¤Áž¨d ­ÁžŽ S ¨ªo 1. PA ‰ B PA  PB  PA ˆ B 2. PA ˆ B PA  PB  PA ‰ B 3. PA B PA ˆ Bc PA  PA ˆ B 4. PB  A PB ˆ Ac PB  PB ˆ A 5. PA ˆ B 0 „˜È °n Á¤Éº° A ¨³ B Áž}œÁ®˜„» µ¦–šr Åɸ ¤Án „—· ¦ªn ¤„œ´ 6. ™oµ A , B ¨³ C Ážœ} Á®˜„» µ¦–rÄ—Ç ÄœÂŽ¤Áž¨d ­ÁžŽ S ¨oª PA‰B‰C PA  PB PC  PAˆB  PAˆC  PBˆC  PAˆBˆC 7. ™µo A Áž}œÁ®˜„» µ¦–Är —Ç ĜŽ¤Ážd¨­ÁžŽ S ¨oª PAc 1  PA 1. Ĝ„µ¦Ã¥œ¨¼„Á˜µq 1 ¨„¼ 1 ‡¦ÊŠ´ ‹Š®µ‡ªµ¤œµn ‹³Ážœ} š‹É¸ ³Å—Âo ˜o¤‹µÎ œªœ‡¸É ®¦°º ‹µÎ œªœÁŒ¡µ³ Ä®o A : šœ ÁŽ˜…°Š‹µÎ œªœ‡šÉ¸ Á¸É „·—…œ¹Ê ‹µ„„µ¦Ã¥œ¨„¼ Á˜qµ B : šœ ÁŽ˜…°Š‹ÎµœªœÁŒ¡µ³šÁ¸É „—· …¹Êœ‹µ„„µ¦Ã¥œ¨¼„Á˜qµ —´ŠœÊœ´ A = ................................................................................................................................. B = ................................................................................................................................. A ‰ B = ................................................................................................................................. PA ‰ B = ................................................................................................................................. 2. „ε®œ—Ä®o A ¨³ B Ážœ} Á®˜»„µ¦–Är —Ç ×¥šÉ¸ PA = 0.4 , PB = 0.5 ¨³ PA ˆ B = 0.2 2.1 PA ‰ B PA  PB  PA ˆ B = .................................................................................................................. 2.2 PAc ˆ B PB  A PB  PA ˆ B = ................................................................................................................. 2.3 PAc ‰ B PAc  PB  PAc ˆ B = ................................................................................................................

⌦ 33 ⌦ 3. „µÎ ®œ—Ä®o A ¨³ B Ážœ} Á®˜„» µ¦–Är —Ç ×¥š¸É PA = 0.3 , PB = 0.6 ¨³ PA ‰ B = 0.8 3.1 PA ˆ B PA  PB  PA ‰ B = ................................................................................................................... = ................................................................................................................... 3.2 PAc ‰ Bc PA ˆ B c = ................................................................................................................... = ................................................................................................................... 3.3 PAc ˆ Bc .................................................................................................................. = ................................................................................................................... = ................................................................................................................... 3.4 PAc ˆ B ................................................................................................................. = ................................................................................................................... = ................................................................................................................... 3.5 PA ‰ Bc .................................................................................................................. = ................................................................................................................... = ................................................................................................................... 4. ‹µ„„µ¦­µÎ ¦ª‹­…» £µ¡…°Šœ„´ Á¦¥¸ œŽŠÉ¹ ¤¸ 40 ‡œ ¡ªµn ¤¸œ´„Á¦¸¥œ­µ¥˜µ­Ê´œ 15 ‡œ ¤¸œ´„Á¦¥¸ œšÉ¸Áž}œ 懢{œ 20 ‡œ ¨³œ´„Á¦¥¸ œšÉ¸Áž}œš´ŠÊ 懢{œÂ¨³­µ¥˜µ­Êœ´ 4 ‡œ ™oµ­n»¤Á¨°º „œ´„Á¦¥¸ œ¤µ®œŠ¹É ‡œ ‹Š®µ ‡ªµ¤œnµ‹³Ážœ} š‹¸É ³Å—oœ„´ Á¦¥¸ œš¸ÁÉ ž}œÃ¦‡¢œ{ ®¦°º 懭µ¥˜µ­œÊ´ Ä®o A šœ ÁŽ˜…°Šœ´„Á¦¥¸ œšÉÁ¸ žœ} 懢œ{ A B B šœ ÁŽ˜…°Šœ´„Á¦¥¸ œšÁ¸É žœ} 懘µ PA ‰ B = ....................................................... = ....................................................... = .......................................................

34 ⌫ ⌫  ⌦  ⌫      5. Ĝ„µ¦­µÎ ¦ª‹„µ¦¨Šš³Á¸¥œª·µ‡–·˜«µ­˜¦r ¢d­·„­r ¨³£µ¬µ°Š´ „§¬…°Šœ„´ Á¦¥¸ œÃ¦ŠÁ¦¥¸ œÂ®nŠ®œÉŠ¹ ‹Îµœªœ 100 ‡œ ¤¸œ´„Á¦¸¥œ¨Šš³Á¸¥œš´ÊŠ 3 ª· µ ‹µÎ œªœ 26 ‡œ ¤Ÿ¸ Á¼o ¦¥¸ œª· µ‡–·˜«µ­˜¦Âr ¨³¢­d „· ­r ‹µÎ œªœ 39 ‡œ ¤¸Ÿ¼oÁ¦¥¸ œª· µ¢d­„· ­Âr ¨³£µ¬µ°´Š„§¬ ˜Ån ¤nÁ¦¥¸ œª·µ‡–·˜«µ­˜¦r ‹Îµœªœ 15 ‡œ ¤Ÿ¸ ¼Áo ¦¥¸ œ 2 ª·µ ‹µ„ 3 ª· µ ‹Îµœªœ 45 ‡œ ¤¸Ÿ¼oÁ¦¸¥œª·µ£µ¬µ°´Š„§¬ ‹Îµœªœ 60 ‡œ ¢d­·„­r ‹µÎ œªœ 59 ‡œ ¨³ Á¦¸¥œÁ¡¥¸ Šª·µÁ—¸¥ª 10 ‡œ ™oµ­¤»n Á¨°º „œ„´ Á¦¥¸ œ‹µ„„¨¤»n ¤µ 1 ‡œ ‹Š®µ‡ªµ¤œµn ‹³Ážœ} šœÉ¸ „´ Á¦¥¸ œ‡œœ¸Ê ‹³Á¨º°„Á¦¥¸ œ 5.1 ª· µ‡–·˜«µ­˜¦r®¦º°¢­d ·„­r 5.2 ª· µ¢d­·„­®r ¦º°£µ¬µ°´Š„§¬ 5.3 ª· µ£µ¬µ°Š´ „§¬®¦º°‡–·˜«µ­˜¦r 5.4 °¥nµŠœ°o ¥ 1 ª·µ‹µ„ 3 ª· µœ¸Ê Ä®o A šœ ÁŽ˜…°Šœ„´ Á¦¸¥œšÁɸ ¨°º „Á¦¥¸ œª· µ AB ‡–˜· «µ­˜¦r B šœ ÁŽ˜…°Šœ„´ Á¦¸¥œšÁ¸É ¨º°„Á¦¸¥œª· µ¢d­·„­r C šœ ÁŽ˜…°Šœ„´ Á¦¥¸ œš¸ÉÁ¨°º „Á¦¸¥œª·µ£µ¬µ°´Š„§¬ C 5.1 PA ‰ B = ........................................................................................................................... = ........................................................................................................................... = ........................................................................................................................... 5.2 PB ‰ C = ........................................................................................................................... = ........................................................................................................................... = ........................................................................................................................... 5.3 PC ‰ A = ........................................................................................................................... = ........................................................................................................................... = ........................................................................................................................... 5.4 PA ‰ B ‰ C = ................................................................................................................... = .................................................................................................................... = .....................................................................................................................

⌦ 35 ⌦  f„®´—š¸É 4 ‡µÎ Âʸ ‹Š œ´„Á¦¥¸ œÂ­—Šª·›š¸ ε˚¥r˜n°ÅžœÊ¸ 1. „ε®œ—Ä®o A ¨³ B Ážœ} Á®˜„» µ¦–r˜°n ޜʸ ×¥šÉ¸ PA 3 , PB 1 ¨³ PA ˆ B 1 82 4 ‹Š®µ 1.1 PA ‰ B 1.2 PAc ¨³ PBc 1.3 PAc ˆ Bc 1.4 PAc ‰ Bc 1.5 PA  B 1.6 PB ˆ Ac 2. ™oµ E Áž}œÁ®˜„» µ¦–Žr Ɋ¹ šµÎ Ä®o°´˜¦µ­ªn œ PE : PEc = 3 : 2 ‹Š®µ PE ¨³ PEc 3. ­»¤n ®¥· Å¡n 1 ĝ ‹µ„ 1 ­µÎ ¦´ ‹Š®µ‡ªµ¤œnµ‹³Ážœ} š‹¸É ³Å—Åo ¡n 3.1 á—Š ®¦°º ᗵΠ3.2 —°„‹·„ ®¦°º K 3.3 …µo ª®¨µ¤˜—´ ®¦º° A 4. Á—µÁ…oµ­°ª· µ‡–˜· «µ­˜¦r¨³£µ¬µÅš¥ ¡ªµn ‡ªµ¤œµn ‹³Áž}œšÁɸ …µ‹³­°Ÿµn œª·µ‡–˜· «µ­˜¦r Ášµn „´ 2 ¨³‡ªµ¤œnµ‹³Ážœ} šÁ¸É …µ‹³­°˜„ª· µ£µ¬µÅš¥ Ášµn „´ 2 ¨³‡ªµ¤œµn ‹³Ážœ} šÁɸ …µ‹³ 53 ­°Ÿnµœ°¥nµŠœo°¥ 1 ª· µ Ášµn „´ 3 ‹Š®µ 5 4.1 ‡ªµ¤œµn ‹³Ážœ} šÉÁ¸ …µ‹³­°Ÿµn œš´ÊŠ­°Šª· µ 4.2 ‡ªµ¤œµn ‹³Ážœ} šÁɸ …µ‹³­°Ÿnµœ°¥nµŠ¤µ„ 1 ª·µ 4.3 ‡ªµ¤œnµ‹³Ážœ} š¸ÉÁ…µ‹³­°Ÿnµœª·µ‡–·˜«µ­˜¦r ˜˜n „ª·µ£µ¬µÅš¥ 4.4 ‡ªµ¤œµn ‹³Ážœ} šÁ¸É …µ‹³­°Ÿµn œª·µ£µ¬µÅš¥ ˜˜n „ª· µ‡–˜· «µ­˜¦r 5. ¤‹¸ —®¤µ¥ 5 Œ´ Ž°Š 5 Ž°Š ŽÉŠ¹ ‹nµ®œµo Ž°ŠÅªÁo ¦¥¸ ¦°o ¥Â¨oª ­»¤n ®¥· ‹—®¤µ¥šÊŠ´ 5 Œ´ Ä­nŽ°Š ‹Š®µ‡ªµ¤œµn ‹³Áž}œš‹É¸ ³Ä­Žn °ŠŸ—· °¥µn Šœ°o ¥ 1 Œ´ 6. ¤‹¸ —®¤µ¥ 4 Œ´ Ä­˜n ¼‹o —®¤µ¥ 6 ˜o¼ ‹Š®µ‡ªµ¤œnµ‹³Ážœ} šÂ¸É ˜¨n ³˜o‹¼ ³Ä­Ån —Åo ¤Án „·œ 1 Œ´ 7. ¤¸‹—®¤µ¥ 6 Œ´ Ä­˜n ¼o‹—®¤µ¥ 5 ˜¼o ‹Š®µ‡ªµ¤œµn ‹³Áž}œšÉ‹¸ ³Ä­‹n —®¤µ¥š„» ˜¼o 8. œÎµ‹—®¤µ¥ 9 Œ´ Şĭn˜¼‹o —®¤µ¥ŽŠ¹É ¤¸°¥n¼ 3 ˜o¼ ‹Š®µ‡ªµ¤œnµ‹³Áž}œš¸É‹³Ä­n˜š¼o ¸®É œÉ¹Š 2 Œ´ ˜šo¼ ­É¸ °Š 3 Œ´ ¨³˜¼šo ­¸É µ¤ 4 Œ´

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⌦ 41 ⌦ 7. ™µo ‡¦°‡¦´ª®œ¹ŠÉ ˜°o Š„µ¦¤¸ »˜¦ 3 ‡œ ‹Š®µ‡ªµ¤œµn ‹³Áž}œšÉ‡¸ ¦°‡¦ª´ œÊ´œ¤¸ »˜¦µ¥ 1 ‡œ „. 1 …. 3 88 ‡. 5 Š. 7 88 8. ‹µ„˜ª´ Á¨… 1 , 2 , 3 , 4 , 5 ‹³­¦µo Š‹Îµœªœª„‡n¼ 3 ®¨„´ ×¥˜´ªÁ¨…˜n¨³®¨„´ ŤnŽÎʵ„œ´ ‹Š®µ‡ªµ¤ œµn ‹³Ážœ} š‹É¸ µÎ œªœ‡¼nª„œÊœ´ ¤¸‡nµ¤µ„„ªnµ 300 „. 1 …. 3 88 ‡. 5 Š. 7 88 9. Ĝ„µ¦ž¦³»¤­´¤¤œµ‡¦ÊŠ´ ®œ¹ŠÉ ¤¸ŸÁ¼o …oµ¦nª¤„µ¦ž¦³¤» ­¤´ ¤œµ 8 ‡œ Ĝ‹Îµœªœœ¤Ê¸  ¸ µÂ —µ¥ – ®·Š 1 ‡¼n ™oµÄœ„µ¦ž¦³»¤­¤´ ¤œµ‡¦Š´Ê œ¸‹Ê —´ Ä®Ÿo o¼¦ªn ¤ž¦³¤» œÉŠ´ ¦°Ã˜p³„¨¤ ‹Š®µ‡ªµ¤œnµ‹³Ážœ} š É¸ µÂ — ‡nœ¼ ʸœÉ´Š˜¦Š…oµ¤„œ´ Á­¤° „. 1 …. 2 7 7 ‡. 1 Š. 2 21 21 10. ˜°o Š„µ¦Á¨º°„„¦¦¤„µ¦ 3 ‡œ ‹µ„‡­n¼ µ¤¸ – £¦¦¥µ 5 ‡n¼ ‹Š®µ‡ªµ¤œµn ‹³Ážœ} š‹É¸ ³Á¨°º „Å—o„¦¦¤„µ¦Å¤n ¤­¸ µ¤Â¸ ¨³£¦¦¥µ‡¼Án —¸¥ª„´œÁžœ} „¦¦¤„µ¦¡¦°o ¤„´œ „. 1 …. 2 33 ‡. 2 Š. 4 99 11. Ä®o A ¨³ B Ážœ} Á®˜»„µ¦–rš¸ÉÁž}œ­´ÁŽ˜…°ŠÂŽ¤Ážd¨­ÁžŽ S ¨³¤¸ PA 0.3 , PB 0.8 , PA ˆ B 0.2 ‹Š®µ PA ‰ Bc „. 0.2 …. 0.4 ‡. 0.5 Š. 0.6 12. ™oµ‡ªµ¤œµn ‹³Ážœ} š¸Éœµ¥ A ­°Á…µo ¤®µªš· ¥µ¨´¥Å—Áo šnµ„´ 3 ¨³‡ªµ¤œµn ‹³Ážœ} šœ¸É µ¥ B ­° 4 Á…µo ¤®µªš· ¥µ¨´¥Å—Áo šnµ„´ 2 PA‰ % 5 ‹Š®µ‡ªµ¤œnµ‹³Áž}œšœ¸É µ¥ A ¨³ œµ¥ B ­°Á…oµ 36 ¤®µª·š¥µ¨´¥Å—o „. 1 …. 1 2 12 ‡. 7 Š. 11 12 12

42 ⌫ ⌫  ⌦  ⌫      13. Ä®o A ¨³ B Áž}œÁ®˜»„µ¦–šr Á¸É ž}œ­´ÁŽ˜…°ŠÂŽ¤Áž¨d ­ÁžŽ S ™µo PA ‰ B 5 , 8 PA ˆ B 1 , PA 1 ¨ªo ‡µn …°Š PB  A ˜¦Š„´…°o ė 32 „. 11 …. 19 24 24 ‡. 1 Š. 3 88 14. Ä®o A ¨³ B Ážœ} Á®˜„» µ¦–šr ¸ÉÁž}œ­´ ÁŽ˜…°ŠÂŽ¤Ážd¨­ÁžŽ S šÉ¸ PA ‰ B 0.8 …o°‡ªµ¤˜°n Şœ¸Ê …°o ė™„¼ ˜o°Š „. PAc ˆ Bc 0.2 …. PAc ˆ B 0.2 ‡. PA ‰ Bc 0.6 Š. PAc ‰ Bc 0.4 15. Ä®o A ¨³ B Ážœ} Á®˜„» µ¦–rš¸ÉÁžœ} ­´ÁŽ˜…°ŠÂŽ¤Áž¨d ­ÁžŽ S š¸É PAc 0.5 ¨³ PA ˆ B 0.3 ¨oª…o°Ä—˜°n Şœ¸ÊŸ·— „. PB ‰ A 0.8 …. PA ˆ Bc 0.2 ‡. PAc ‰ Bc 0.7 Š. PAc ˆ Bc 0.4 16. Ä®o A , B ¨³ C Ážœ} Á®˜„» µ¦–ršÁ¸É žœ} ­´ÁŽ˜…°ŠÂŽ¤Ážd¨­ÁžŽ S š¸É A ‰ B ‰ C S ‹Š¡‹· µ¦–µ ªnµ…°o ‡ªµ¤˜n°Åžœ¸…Ê o°Ä—™„¼ ˜o°Š „. PA PB 1 3 …. ™µo PA a ¨³ PB b ¨ªo PA ‰ B a  b  ab ‡. ™oµ PA ˆ B I ¨ªo PA I ®¦°º PB I Š. ™oµ A , B , C Ážœ} Á®˜»„µ¦–šr Å¸É ¤nÁ„—· ¦ªn ¤„œ´ ¨ªo PA  PB  PC 1 17. ™oµ A ¨³ B Ážœ} Á®˜„» µ¦–Žr ¹ÉŠ PA ‰ B 3 , PAc 2 ¨³ PA ˆ B 1 ¨ªo 3 4 4 …o°Ä—˜°n ŞœŸÊ¸ ·— 1 …. PAc ˆ B 5 „. PB 2 8 Š. PAc ‰ Bc 12 3 3 ‡. PA ˆ Bc 4

⌦ 43 ⌦ 18. ‹µ„„µ¦­»¤n ‡¦°‡¦´ªÄœ®¤n¼ µo œ¤µ 1 ‡¦°‡¦´ª ¡ªµn ‡ªµ¤œnµ‹³Ážœ} šÉ¸‡¦°‡¦ª´ œÊœ´ ¤°¸ µ¡¸ Á¨¸Ê¥ŠÅ„n Ášnµ„´ 0.5 ‡ªµ¤œnµ‹³Ážœ} š¸É‡¦°‡¦ª´ œ´Êœ¤¸°µ¡¸ Á¨¸Ê¥Š®¤¼ Ášnµ„´ 0.6 ¨³‡ªµ¤œµn ‹³Ážœ} š¸É ‡¦°‡¦ª´ œœÊ´ ¤¸°µ¸¡Á¨¥Ê¸ ŠÅ„Ân ¨³®¤¼ Ášµn „´ 0.3 ™µo ®¤¼n µo œÂ®nŠœ¤¸Ê ¸ 300 ‡¦°‡¦ª´ ‹Š®µªµn ¤„¸ ɸ ‡¦°‡¦´ªšÁ¸É ¨Ê¥¸ ŠÅ„®n ¦°º ®¤¼ „. 180 ‡¦°‡¦´ª …. 210 ‡¦°‡¦´ª ‡. 240 ‡¦°‡¦´ª Š. 270 ‡¦°‡¦´ª 19. œ„´ Á¦¸¥œ„¨¤n» ®œ¹ŠÉ ˜o°Š­°ª·µ‡–˜· «µ­˜¦r ¨³Á‡¤¸ Ÿ¨ž¦µ„’ªµn ‡ªµ¤œµn ‹³Áž}œš¸É­°Ÿnµœª· µ ‡–·˜«µ­˜¦r Ášnµ„´ 1 ‡ªµ¤œnµ‹³Ážœ} šÉ­¸ °Ÿµn œª·µÁ‡¤¸ Ášµn „´ 3 ‡ªµ¤œnµ‹³Ážœ} š­É¸ °ŸnµœÁ¡¸¥Š 35 ­°Šª· µ Ášµn „´ 1 ™µo ­¤n» œ„´ Á¦¥¸ œ¤µ 1 ‡œ ‹Š®µ‡ªµ¤œµn ‹³Ážœ} š‹É¸ ³Å—oœ„´ Á¦¸¥œš¸É­°Ÿµn œ°¥nµŠ 15 œo°¥®œÉ¹Šª·µ „. 11 …. 12 15 15 ‡. 13 Š. 14 15 15 20. ®¤n¼ µo œÂ®Šn ®œÉ¹Š¤¸ 600 ‡¦°‡¦ª´ ž¦³„°°µ¡¸ šÎµœµ 320 ‡¦°‡¦ª´ šÎµÅ¦n 210 ‡¦°‡¦´ª šµÎ œµÂ¨³šµÎ Ŧn 190 ‡¦°‡¦´ª Á¤°Éº ­n¤» ‡¦°‡¦ª´ Á®¨µn œ¸¤Ê µ 1 ‡¦°‡¦ª´ ‹Š®µ‡ªµ¤œnµ‹³Ážœ} šÉ¸­¤»n ŗo‡¦°‡¦ª´ šÅ¸É ¤nž¦³„°°µ¸¡šµÎ œµÂ¨³Å¤nž¦³„°°µ¸¡šÎµÅ¦n „. 13 …. 17 30 30 ‡. 19 Š. 53 60 60 -------------------------------------------------------------------

44 ⌫ ⌫  ⌦  ⌫      ÁŒ¨¥‡Îµ˜°Â „f š„´ ¬³ 1. „ 11. „ 2. „ 12. ‡ 3. „ 13. ‡ 4. … 14. „ 5. „ 15. Š 6. … 16. Š 7. … 17. ‡ 8. ‡ 18. ‡ 9. „ 19. ‡ 10. … 20. „