The National Cancer Institute estimates that 3.65% of women in their 60s get breast cancer. A mammogram can typically identify correctly 85% of cancer cases and 95% of cases without cancer. What is the probability that a woman in her 60s who has a positive test actually has breast cancer?

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Positive test.

Event B: Having breast cancer.

3.65% of women in their 60s get breast cancer

This means that

A mammogram can typically identify correctly 85% of cancer cases

This means that

Probability of a positive test.

85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So

What is the probability that a woman in her 60s who has a positive test actually has breast cancer?

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer

there is no question content here, but you for the free points! : d