Solution

So ... what is the probability that a woman is truly sick when she has a positive mammogram? The answer is the ratio of sick women who have tested positive to all women who have tested positive, and can be expressed with the following formula:

p(sick|pos) = a / (a+b)

"P" stands for "probability", "pos" for a positive mammogram and "|" for given. "A" represents the number of people who have tested positive and are really sick, while "b" indicates those who have tested positive but are healthy.

We know that a = 7 and b = 70, therefore:

p(sick|pos) = 7/77 = 9 %.