Question

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?

Answer 1

Answer:

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