Assume breast cancer affects 0.006 of the female population between 45 and 55 ye

Question

Assume breast cancer affects 0.006 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

0.93 accurate detecting people who actually have breast cancer (true positive rate)

0.93 accurate for people who do not have breast cancer (true negative rate).

Question:

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.

Explanation / Answer

probability that a female between the ages of 45 and 55 test positive =P( have breast cancer and test positive+do not have breast cancer and test posiitve) =0.006*0.93+(1-0.006)*(1-0.93)=0.07516

hence  probability that a female between the ages of 45 and 55 has breast cancer given tested postiive

=P( have breast cancer and test positive)/P( tested positive) =0.006*0.93/0.07516=0.0742

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