1% of women at age 40 who participate in routine screening have breast cancer. 80% of women with breast cancer get positive mammographies. 9.6% of women without breast cancer get positive mammographies. A 40-year old woman participates in routine screening and has a positive mammography. What's the probability she has cancer?

0.0776

Step-by-step explanation:

In order to solve this problema, Baye's rule is used. Ii is expressed as follows:

P (A if B) = (P (B if A) * P (A)) / (P (B))

Let A be women who have cancer and let B be women who have positive mammographies

So, P (B if A) would be women with breast cancer get positive mammographies

P (B if A) = 0.8

P (A) would be women with breast cancer

P (A) = 0.01

P (B) would be the women with positive mammographies. We don't know it.

In order to find it we use law of total probability

P (B) = P (positive mammographies and cancer) + P (positive mammographies without cancer)

P (B) = 0.8*.01+0.096*0.99

P (B) = 0.103

With P (B) calculated we can complete the equation:

P (A if B) = (0.8*0.01) / 0.103=0.0776

Probability is 0.0776