Probabilities basic elements

T Stella Seremetaki Probabilities Train yourself to learn Mathematics

Stella Seremetaki, Mathematician Contents PROBALITY.............................................................. 1 Events ......................................................................... 1 A probability distribution .............................. 1 An example of a probability function is given in the table ................................................. 2 the sample space Ω.............................................. 2 PROBALITY Recap The collection of all possible outcomes is called the sample space The probabilities inside a sample space must add up to 1 Events are groups of one or more outcomes Two events are mutually exclusive if they czn not happen together. If A and B are mutually exclusive events then 2

Stella Seremetaki, Mathematician P(A AND B)=0 P(A OR B)=P(A)+P(A) The probabilities of all the possible nutually axclusive events add up to 1 A probability distribution is a table or function that gives the probability of all possible outcomes Outcome A B CD Probability 0.2 k 3k 0.1 of outcome An example of a probability function is given in the table. The probability function is given in the table. The probability of event A occurring is 0.2 You could write this P(A)=0.2 Since the probabilities must add up to 1 0.3+4k=1->k=0.175 Therefore the rest of the probabilities are P(B)=0.175 P(C) =0.525 Verification : P(A)+P(B)+P(C)+P(D)=1 3

Stella Seremetaki, Mathematician Two events are independent if they have no effect on each other If events A and B are independent then P(A and B)=P(A)XP(B) Notes A  B is the intersection between A and B, For example they both happen A  B is the union of A and B for example at least one of them happens References Edexcel A Level Maths , Year 1 and Year 2 Statistics student book, Powered by My Maths.co.uk the sample space Ω ACB 4