NotesStat5_4

NotesStat5_4 - 5.4 Sullivan Statistics Notes 1. Basic...

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1. Basic Conditional Probability In 5.4 we first introduce the conditional probability rule. P ( A | B ) = ) ( ) ( B P B A P P( A | B ) means “what is the probability of A given B occurs”. If events A and B are not independent we call the events dependent. The property P(A | B) P(A) will be true if the events are dependent. In other words the fact B occurs effects the probability A occurs. An example can be motivated by a contingency (or joint frequency) table: Example 1) We survey 100 HS senior males about their college plans and their family background. We examine how a father’s education may affect a son’s plan. Let A = father is college educated B = A C = father is not college educated D = son goes to college E = D C = son doesn’t go to college Father College Educated Father Not College Educated Son goes to College 30 10 Son doesn’t go to College 20 40 If we simply ask the question P(D) “the probability the son goes to college” we see that 30 + 10 sons go to college while 20 + 40 do not. So 40 of 100 sons go to college. P(D) = 40 . 0 100 40 = On the other hand if the father is college educated the plans of the son seems to be effected. Of 50 college educated fathers 30 of the sons go to college. P(D | A) =
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NotesStat5_4 - 5.4 Sullivan Statistics Notes 1. Basic...

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