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Unformatted text preview: × 0.60 = 0.42 . 2. (4) Alex is a naughty student – he does not always study for his exams. There is only a 60% chance that he would study for an exam. If he does study for an exam, the probability that he would pass it is 0.70. However, if he does not study, there is an 80% chance he would fail. Suppose you find out that Alex failed an exam. What is the probability that he did study for it? P ( S ) = 0.60, P ( P  S ) = 0.70, P ( F  S ' ) = P ( P '  S ' ) = 0.80. Need P ( S  F ) = ? P F = P ' Total S 0.60 ⋅ 0.70 0.42 0.18 0.60 S ' 0.08 0.40 ⋅ 0.80 0.32 0.40 Total 0.50 0.50 1.00 P ( S  F ) = 50 . 18 . = 0.36 . OR P ( S  F ) = ( ) ( ) F P F S P ∩ = 32 . 18 . 18 . + = 50 . 18 . = 0.36 . OR Bayes’ Theorem: P ( S  F ) = ( ) ( ) ( ) ( ) ( ) ( ) ' ' S F P S P S F P S P S F P S P ⋅ ⋅ ⋅ + = 80 . 40 . 30 . 60 . 30 . 60 . ⋅ ⋅ ⋅ + = 50 . 18 . = 0.36 ....
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 Spring '08
 Kim
 Statistics, Probability, Alex, Bayesian probability

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