Assume breast cancer affects 0.005 of the female population between 45 and 55 years of age....

Assume breast cancer affects 0.005 of the female population between 45 and 55 years of age. There are two kinds of positive test results: -True positive (the test indicates you have a disease, and you actually have it) -False positive (the test indicates you have a disease, but you actually do not) Assume mammograms are: 0.932 accurate detecting people who actually have breast cancer (true positive rate) 0.91 accurate for people who do not have breast cancer (true negative rate) Compute the probability that a female between the ages of 45 and 55 who tests positive for breast cancer has breast cancer, and enter your answer with 3 decimal places.

Expert Solution

P(have breast cancer) = 0.005

P(positive test | have breast cancer) = 0.932

P(negative test | don't have breast cancer) = 0.91

P(positive test | don't have breast cancer) = 1 - P(negative test | don't have breast cancer) = 1 - 0.91 = 0.09

P(positive test) = P(positive test | have breast cancer) * P(have breast cancer) + P(positive test | don't have breast cancer) * P(don't have breast cancer)

= 0.932 * 0.005 + 0.09 * (1 - 0.005)

= 0.0942

P(has cancer | positive test) = P(positive test | have breast cancer) * P(have breast cancer) / P(positive test)

= 0.932 * 0.005 / 0.0942

= 0.049 (ans)

orchestra answered 2 years ago

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