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

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

.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.  

Explanation / Answer

Probability of females who have breast cancer, P(B) = 0.006

Probability of females who have do not breast cancer, P(B') = 1- 0.006 = 0.994

Probability of females who have breast cancer and test positive P(B and +) = 0.006 * 0.94 = 0.00564

Probability of females who have do not breast cancer and test positive P(B' and +) = 0.994 * (1 - 0.91)

= 0.08946

Probability of testing positive, P(+) = 0.00564 + 0.08946 = 0.0951

Probability that a female between the ages of 45 and 55 who tests positive for breast cancer has breast cancer, P( B | +) = P( B and +) / P(+)

= 0.00564 / 0.0951

= 0.0593

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