A certain form of cancer is known to be found in women over 60 with probability 0.07. A blood test exists for the detection of the disease, but the test is not infallible. In fact, it is known that 10% of the time the test gives a false negative (i.e., the test incorrectly gives a negative result) and 5% of the time the test gives a false positive (i.e., incorrectly gives a positive result). If a woman over 60 is known to have taken the test and received a favorable (i.e., negative) result, what is the probability that she has the disease?

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Chapter1: Combinatorial Analysis
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A certain form of cancer is known to be found in women over 60 with probability 0.07. A blood test exists for the
detection of the disease, but the test is not infallible. In fact, it is known that 10% of the time the test gives a false
negative (i.e., the test incorrectly gives a negative result) and 5% of the time the test gives a false positive (i.e.,
incorrectly gives a positive result). If a woman over 60 is known to have taken the test and received a favorable (i.e.,
negative) result, what is the probability that she has the disease?
Select one:
O a. 0.9917
O b. 0.0358
O c. 0.215
O d. 0.00786
Transcribed Image Text:A certain form of cancer is known to be found in women over 60 with probability 0.07. A blood test exists for the detection of the disease, but the test is not infallible. In fact, it is known that 10% of the time the test gives a false negative (i.e., the test incorrectly gives a negative result) and 5% of the time the test gives a false positive (i.e., incorrectly gives a positive result). If a woman over 60 is known to have taken the test and received a favorable (i.e., negative) result, what is the probability that she has the disease? Select one: O a. 0.9917 O b. 0.0358 O c. 0.215 O d. 0.00786
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