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9.6 Bayes' Formula

9.6 Bayes' Formula - 9.6 Bayes Formula IfP(E F),(F E...

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9.6 Bayes’ Formula If P(E F) is known for two events E and F, then Bayes’ formula allows us to find  P(F E).   Bayes’ Formula:   ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ... i i i n n P F P E F P F E P F P E F P F P E F × = × + + × 1 1 .  Using a tree diagram, the numerator is the  product of the probabilities of arriving at the particular outcome  ( 29 i P F E and the denominator is the sum of the products of each branch leading to outcome E. 1. For two events E and F, P(E) = .35, P(F|E) = .6, and P(F|E’) = .2.  Find: a. P(E F) b. P(E F’) c. P(E’|F) d. P(E’|F’) 2. A scientist is 75% confident that hypothesis A is true and is 90% confident that event B will occur if event  A has occurred but only a 50% chance of occurring if A has not occurred:   P (A)  = .75,   P (B|A)  = .9, and P(B| A’) = .5.   Find: a. P(A B) b. P(A B’) c. P(A’|B) d. P(A’|B’) 3. On a given weekend, a company can buy television advertising time for a college football game, a baseball 
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