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?

Answer:0.0079 is the probability that woman has cancer when the test were negative.Step-by-step explanation:We are given the following information in the question:Let A be the event when the patient have cancer and B be the event when test result is positiveP(A) = 0.07 Bayes Theorem:[tex]P(A|B') = \displaystyle\frac{P(B'|A)P(A)}{P(B'|A)P(A) + P(B'|A')P(A')}[/tex][tex]P(B'|A) = 10\% = 0.10\\P(B|A') = 5\% = 0.05[/tex]We have to find the probability that she has disease when test were negative that is we have to find:[tex]P(A|B')[/tex]Putting all the values in the above formula, we have,[tex]P(A|B') = \displaystyle\frac{0.10\times 0.07}{0.10\times 0.07 +(1- 0.05)\times 0.93} = 0.0079[/tex]Thus. 0.0079 is the probability that woman has cancer when the test were negative.