Question 8 (Mandatory) (12 points) Assume breast cancer affects 0.007 of the fem

Question

Question 8 (Mandatory) (12 points) Assume breast cancer affects 0.007 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 0.94 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.

Explanation / Answer

probabilty of positive test =P(Disease)*P(test positive|Disease)+P(Not disease)*P(test positive|not disease)

                      =0.007*0.94+(1-0.007)*(1-0.91)=0.09595

hence P(Disease|test positive)=P(Disease and test positive)/P(test positive) =0.007*0.94/0.09595=0.06858

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