Question

In the general? population, one woman in

ten

will develop breast cancer. Research has shown that 1 woman in

650

carries a mutation of the BRCA gene.

Nine

out of 10 women with this mutation develop breast cancer.

?(a) Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene.

The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is

nothing .

?(Round to one decimal place as? needed.)

?(b) Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer.

The probability that a randomly selected woman will carry the gene mutation and develop breast cancer is

nothing .

?(Round to four decimal places as? needed.)

?(c) Are the events of carrying this mutation and developing breast cancer independent or? dependent?

Dependent

Independent

Answer 1

P(breast cancer) = 1/10 = 0.1

P(mutation) = 1/650 = 0.0015

a) P(breast cancer | mutation) = 9/10 = 0.9

b) P(mutation and breast cancer) = P(breast cancer | mutation) * P(mutation)

                                                      = 0.9 * 0.0015 = 0.0014

c) P(breast cancer) * P(mutation) = 0.1 * 0.0015 = 0.00015

As P(mutation and breast cancer) P(breast cancer) * P(mutation), so the two events are not independent. They are dependent.