Question Help In the general population, one woman in eight will develop breast

Question

Question Help In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman in 650 carries a mutation of the BRCA gene. Eight 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 arry 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? Independent

Explanation / Answer

A) P(selected woman will develop breast cancer | has a mutation of the BRCA gene)

= P(woman will develop breast cancer and has a mutation of the BRCA gene) / P(has a mutation of the BRCA gene)

= 8/10 = 0.8

B) P(woman will carry the mutation of the BRCA gene and will develop breast cancer) = 0.8 * 1/650 = 0.0012

C) P(events carrying mutation) * P(developing Breast cancer) = 1/650 * 1/8 = 0.0002

P(events carrying mutation and developing Breast cancer) = 0.0012

As these two probabilities are not equal,so the events are dependent.

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