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Unformatted text preview: (0 . 40)(0 . 70) (0 . 40)(0 . 70) + (0 . 90)(0 . 30) ≈ . 50901 62. Let B be the event that the purchasher has a basic model, let D be the event that the purchaser has a deluxe model. Let E be the event that the purchaser has an extended warranty. We are given that P ( B ) = 0 . 40 (and hence we know that P ( D ) = 0 . 60) and we are given that P ( E  B ) = 0 . 30 , P ( E  D ) = 0 . 50 . So, we know that P ( E  B ) = 0 . 70 , P ( E  D ) = 0 . 50 . The answer, by Bayes Rule, is then P ( B  E ) = P ( E  B ) · P ( B ) P ( E  B ) · P ( B ) + P ( E  D ) · P ( D ) = (0 . 30)(0 . 40) (0 . 30)(0 . 40) + (0 . 50)(0 . 60) ≈ . 2857...
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 '08
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 Conditional Probability, randomly selected tick

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