ความน่าจะเป็น. สสวท.

3| 4 72 3 4

3| 4 73 1. 2. 3. 3.1 k 1. n1 n2 1 2 k nk k n1 n2 nk 2. k

3| 4 74 n1 1 1 1 2 n2 3 n3 2 1 k1 k nk 1n k n1 n2 nk n n 3. n r n! 4. r Pn, r n! (n r)! 5. n Cn, r n! (n r)!r! 3.2

3| 4 75 1. 0 2 1 41 2. 3.

3| 4 76 1. 2. 3. 4. 5. 6. 1. 2. 3. 4. 5.

3| 4 77 1

3| 4 78 2 1234561 2 3 4 5 1 2 3 4 5 6 7 8 9 10 11 2

3| 4 79 23 1 2 2 – 1 1 – 2 3 1 1 2 2 3

3| 3 4 – 3 80 – 2 12 1 1 2 3 4 5 6 2 21 22 32

3| 4 81 5 43 3.1 6 1, 2, 3, 4, 5 6 5.

3| 4 82 10 1) 2) 3) 1. 3 1, 2 3 2. 3.

Pn, r 3| n 4 83 0! 1 n! n n 1 n 2 ... 1 1. 4 2 2. 4

3| 4 84 2 3. 3 4. Cn, r 9. 1) 2)

3| 4 85 3.3 16

3| 4 86 1. 2. 3. 4. 5. 6. 7. 8. 9. 1. 33 7 33 7 2. 7 33 72 3. 33 73 4. 7 33 74 5. 7 33 75 6. 7 33 76 7. 33 77 8. 7 9. 7 33 76 33 77 264 76

3| 4 87 30 / / 1. “ ” 2. 1. “” 2. 3–4 3. 1–9 4. 5.

3| 4 88 4 3 3.4 3.1 1, 2 3.1 4 – 8 3.2 1 – 5 3.3 1 – 6

3.5 3| 3 4 89 1. 4 2. 3. 4 43

3| 4 90 1. 2. 3. 4. 5. 1) 2) 6. 7. 8. 9. 1) 2) 10. 11. 12. 13.

3| 4 91 14. 15. 1) 2) 16. 17.

3| 4 92 Permutation “ 3.6 Prn , n Pr , nPr P n, r Combination P Pn, r “ ” ” Crn , n Cr , nCr C n, r C Cn, r 3.7 3 4 1. AB A 2 2 C C A B 2. CB 3 3

3| 4 93 3. 4 09 4. 09 3 5. 4 3 7 1 1 1 8 7 6. 7 7. 1 8. 10 9. A 7 4 3 10. 9 3 ( 25252) 3 19 11.

3| 4 94 1. A B 12 2C 1 AC 2 2 CB 3 AB C 23 6 AB 268 2. 2 13 3 2 22 4 3 4 12 3. 2 1 12 14 2 26 4 26 104

3| 4 95 2 09 10 10 10 1,000 4. 09 104 1000 104,000 3 123 1 1 3 0, 2, 4, 6, 8 5 2 1 2 0, 1, 2, …, 9 9 3 1 1 0, 1, 2, …, 9 29 5 9 9 405 5. 1 3 1 14 2 13 3 4 3 12 4 3 12 19 22 1 14 5

3| 4 96 21 3 4 5 4 20 20 1 19 6. 7 7 1 P77 5, 040 78 7. 1 P8,7 40,320 8. 10 3 9. A 7 C10,3 120 4 C7,4 35 10. 9 13 9 6 C9 , 3 9! 6!3! 23 1 C6 , 3 6! 3!3!

3| 4 97 33 32 1 9 33 3 9! 6! 1 1,680 6!3! 3!3! 11. 12345 13 C5,3 10 1, 2, … , 9 21 19 3 1 1, 2, … , 9 2 8 19 5 10 9 8 720 3.8 4 2 2 1

3| 4 98 3.1 2) 30 2) 810 1. 25 2) 360 2. 13 3. 90 2) 90 4. 1,738,283,976 4) 1 5. 1) 6 3) 30 6. 1) 900 3) 90 7. 676 8. 1) 1,296 3.2 1. 362,880 2. 1) 1,680 3) 120 3. 24

4. 15,120 3| 5. 120 4 99 3.3 1. 56 2) 70 2. 15 2) 12 3. 21,162,960 2 4. 1) 1,001 2) 18,720 3) 210 5. 45 6. 1) 676 3) 0 1. 22 2. 6 3. 15,600 4. 10,156,250 5. 1) 25,974 6. 109,879,011

3| 4 100 2) 30 7. 60 2) 21 8. 1,024 9. 1) 6 10. 360 11. 5,527,200 12. 45 13. 300 14. 2,400 15. 1) 45 16. 399,000 17. 34

4| 4 101 4 4 1. 2.

4| 4 102 4.1 1. 2. 3. 4. S S ES E PE PE nE nS nE E nS S

4.2 4| Galton board 4 103 1. Galton board Galton board 2. 100 Galton board Galton board 3. Galton board 4.

4| 4 104 Galton board o o o

4| 4 105 The Last Banana The Last Banana 1. 3 – 4 The Last Banana 22 1 The Last Banana The Last Banana 1, 2, 3 4 2 56 The Last Banana 2. 3. The Last Banana 12

4| 4 106 1 2 4. 4 o o 4 5.

4| 4 107 4.2 5 3 5. 2 1 2 () 1 () 4.3 1984 – 1986 Let’s “ Monty Hall Monty Hall Problem Monty Hall Problem Make a Deal 1, 2 3 1 1 ”

4| 4 108 1. 2. goo.gl/9c2kWZ 3. 1, 2 3 1 1 4. 30 X

4| 4 109 1 11 21 2 12 22 3 13 23 4 14 24 5 15 25 6 16 26 7 17 27 8 18 28 9 19 29 10 20 30 5. 4 30 6. 30 X

4| 4 110 1 11 21 2 12 22 3 13 23 4 14 24 5 15 25 6 16 26 7 17 27 8 18 28 9 19 29 10 20 30 7. 6 8. 30

4| 4 111 Monty Hall Problem 1. 2. – 3. – 4. 1X 11 X 21 X 2X 12 X 22 X 3X 13 X 23 X 4X 14 X 24 X 5X 15 X 25 X 6X 16 X 26 X 27 X 7X 17 X 28 X 8X 18 X 29 X 9X 19 X 30 X 10 X 20 X 5. 4 30 7 0.23 30

4| 4 112 6. 1X 11 X 21 X 2X 12 X 22 X 3X 13 X 23 X 4X 14 X 24 X 5X 15 X 25 X 6X 16 X 26 X 7X 17 X 27 X 8X 18 X 28 X 9X 19 X 29 X 10 X 20 X 30 X 7. 6 30 20 0.67 8. 8 30 1) 57 57

2. 4| (experimental probability) 4 113 Monty Hall Problem 50 1 / goo.gl/9c2kWZ 1. “Monty Hall Problem” 2. Monty Hall Problem 1. Monty Hall Problem 2. “Monty Hall Problem” 3. 4. 1

4| 4 goo.gl/9c2kWZ 3–7 114 Monty Hall Problem 5. 6. 7. 8 8. (empirical probability) 8 9. 4.4 4 4

4.5 4| 4 4 115 1. 4.1 1 – 3 2. 4.2 1 – 8 4 4 4 4

4| 4 116 1. 1) 2) 3) 4) 5) 2. 1) 2) 3. 1) 2) 3) 4) 5) 4. 1) 2) 3) 4) 5)

4| 4 117 5. 1) 2) 3) 6. 1) 2) 3) 4) 5) 6) 7. 8. 9. 1) 2) 3) 10. 1) 2) 11.

4| 4 118 12. 13. 14. 1) 2) 15. 16. 17. 18. 1) 2) 3) 19. 20. 21. 22. 23. 1) 2) 3)

4| 4 119 4) 24. 25. 4.6 4 4 1. 1 5 2. 4 1 3. ( –) A, B, AB, O

4| 4 120 1 4. 5. 1 ( 5 25 6. 23456, 76543 ) 12 40 9 20 7. 1 3 8. 10 1 10 17 3 9. 3 1) 4 09 2)