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Unformatted text preview: Now suppose that your test comes back positive. What you want to know is, what are the chances that you have this type of cancer? A common wrong answer – that the chance is about . 95 – is very much wrong! Solution: Let A 1 = Has Cancer A 2 = Does not have cancer Clearly, P ( A 1 ) = 5 1 , 000 , P ( A 2 ) = 995 1 , 000 and B = Tested Positive With P ( B  A 1 ) = . 95 , P ( B  A 2 ) = . 05 By Baye’s Rule P ( A 1  B ) = P ( B  A 1 ) P ( A 1 ) P ( B  A 1 ) P ( A 1 ) + P ( B  A 2 ) P ( A 2 ) = . 95 × 5 1 , 000 . 95 × 5 1 , 000 + . 05 × 995 1 , 000 = . 087 That is, even your test comes back positive, the chances you have this type of cancer is just 8.7%. 1...
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This note was uploaded on 04/16/2010 for the course STAT 427 taught by Professor Staff during the Spring '08 term at Ohio State.
 Spring '08
 Staff
 Probability

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