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# lec13 - STATISTICS 13 STATISTICS Lecture 13 Oct 25 2010...

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STATISTICS 13 STATISTICS 13 STATISTICS 13 Lecture 13 Lecture 13 Oct. 25, 2010 Oct. 25, 2010

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Review Combination Events relation Union Intersection Complement Calculation of probability --For union: additive rule --For complement
Example: Birthday Problem Suppose there are n people (n<365) in a room, what is the probability that at least two of them have a common birthday? (assume no one has birthday on Feb. 29) By multiplicative rule, number of outcomes N in sample space is N= , and all simple events are equally likely A=at least two people have a common birthday; the number of outcomes in A is hard to count directly.

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Example: Birthday Problem (Cont.) n P(A) 4 0.016 16 0.284 23 0.507 40 0.891 56 0.988
Conditional Probability The probability that A occurs, given that event B has occurred, is called the conditional probability of A given B, and is defined as 0 ) ( if ) ( ) ( ) | ( B P B P B A P B A P S A B B A

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Example : Fruit Fly In the fruit fly example, suppose that a randomly selected fly has normal wing size. What is the probability that it
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