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P0065_Soln - P R 1 R 2 29 PR 1 R 2 29 PR 1 R 2 29 P R 1 R 2...

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P0065_Soln.doc The probability that the 1 st radiologist detected the disease is P R 1 ( 29 = 2 3 When the 1 st radiologist detected the disease, the 2 nd radiologist might or might not have detected it. So… PR 1 R 2 ( 29 + PR 1 R 2 ( 29 = 2 3 Similarly, when the 2 nd radiologist detected the disease, the 1 st radiologist might or might not have detected it. So… PR 1 R 2 ( 29 + P R 1 R 2 ( 29 = 1 2 The probability that “at least one” of the radiologists detected it refers to the summation of three possibilities: 1 st radiologists did and 2 nd didn’t, 1 st radiologists didn’t but 2 nd did, or they both detected it. PR 1 R 2 ( 29 + P R 1 R 2 ( 29 + PR 1 R 2 ( 29 = 3 4 We want to know the probability that the 2 nd radiologists detected the disease given that we know that only one of the two radiologists did: P R 1 R 2 R 1 R 2 , R 1 R 2 { } ( 29 P R 1 R 2 R 1 R 2 , R 1 R 2 { } ( 29 = P R 1 R 2 R 1 R 2 , R 1 R 2 { } ( 29 P R 1 R 2 , R 1 R 2 { } ( 29 = P R 1 R 2 ( 29 P R 1 R 2 , R 1 R 2 { } ( 29 = P R 1 R 2 ( 29 P R 1 R 2 ( 29
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Unformatted text preview: P R 1 R 2 ( 29 + PR 1 R 2 ( 29 PR 1 R 2 ( 29 + P R 1 R 2 ( 29 + PR 1 R 2 ( 29 = 3 4 PR 1 R 2 ( 29 + PR 1 R 2 ( 29 = 2 3 PR 1 R 2 ( 29 + P R 1 R 2 ( 29 + PR 1 R 2 ( 29-PR 1 R 2 ( 29 + PR 1 R 2 ( 29 ( 29 = 3 4-2 3 P R 1 R 2 ( 29 = 9 12-8 12 = 1 12 PR 1 R 2 ( 29 + P R 1 R 2 ( 29 + PR 1 R 2 ( 29 = 3 4 PR 1 R 2 ( 29 + P R 1 R 2 ( 29 = 1 2 PR 1 R 2 ( 29 + P R 1 R 2 ( 29 + PR 1 R 2 ( 29-PR 1 R 2 ( 29 + P R 1 R 2 ( 29 ( 29 = 3 4-1 2 PR 1 R 2 ( 29 = 3 4-1 2 = 9 12-6 12 = 3 12 P0065_Soln.doc P R 1 R 2 R 1 R 2 , R 1 R 2 { } ( 29 = P R 1 R 2 ∩ R 1 R 2 , R 1 R 2 { } ( 29 P R 1 R 2 , R 1 R 2 { } ( 29 = P R 1 R 2 ( 29 P R 1 R 2 ( 29 + PR 1 R 2 ( 29 = 1 12 1 12 + 3 12 = 1 4 Refer to B&T Example 1.8...
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