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Finite Chapter 7.5

Finite Chapter 7.5 - Math 120 SP08 SBrodnick 7.5...

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Math 120 SP08 SBrodnick 1 1 7.5 : Conditional Probability & Independence 2 7.5: Conditional Probability & Independence * Entrées and desserts served at a charity event that 250 people attended: Prob. a person who had cheesecake had pork? Rephrased: Prob. a person had pork, given that he or she had cheesecake? 250 80 170 Total 150 45 105 Ice Cream (I) 100 35 65 Cheesecake (C) Total Beef (B) Pork (R) 65/100 3 * This is called conditional probability For this example, we write P(R | C), where P(R|C) = = = * In general, for events A and B (where P(B) ≠ 0) P(A|B) = * (back to table) P(B|I) = P(C|R) = P(B|C) = P(R C) P(C) P(A B) P(B) 65/250 100/250 65 100 “prob. of R given C” 7.5: Conditional Probability & Independence 45/150 65/170 35/100 4 * A and B are independent if the outcome of one does not affect the outcome of the other * Mathematically, P(A B) = P(A) · P(B) (use this to test for independence) Examples : 1. Suppose P(E) = 0.7, P(F) = 0.8, and P(E F) = 0.6 Find P(E|F) and P(F|E). 2.Let A and B be independent events with P(A) = 2/5 and P(B) = 3/4.

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Finite Chapter 7.5 - Math 120 SP08 SBrodnick 7.5...

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