In the general population, one woman in ten will develop breast cancer. Research

Question

In the general population, one woman in ten will develop breast cancer. Research has shown that 1 woman in 550 carries a mutation of the BRCA gene. Eight 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 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 (Round to four decimal places as needed.) (c) Are the events of carrying this mutation and developing breast cancer independent or dependent? O Dependent O Independent

Explanation / Answer

Pr(Breast Cancer) = 1/10

Pr(Carries a mutation of BRCA gene) = 1/550

Pr(Breat cancer l carries a BRCA gene) = 8/10 = 0.8

(a) Pr(A randolmly selected woman will develop breast cancer given she has a mutation of BRCA gene) = 0.8

(b) Pr(Carry the mutation of BRCA gene and will develop breast cancer) = 1/550 * 8/10 = 8/5500 = 0.0015

(c) These two events will be independet if

Pr(Mutation and devaloping breast cancer) = Pr(Mutation) * Pr(developing breast cancer)

Pr(Mutation) = 1/550

Pr(developing breast cancer) = 1/10

Pr(Mutation and developing breast cancer) = 8/5500

so these two events are not independent as the equality relation doesn't hold true.

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