In the general population one woman in eight will develop br

In the general population, one woman in eight will develop breast cancer. Research has shown that I 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? Dependent Independent

Solution

a)

As given,

P(cancer|mutation) = 8/10 = 0.8 [ANSWER]

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b)

P(mutation and cancer) = P(mutation) P(Cancer|mutation)

= (1/650)*(8/10)

= 0.001230769 [ANSWER]

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c)

They are DEPENDENT. [ANSWER]

This is so as P(cancer) =/= P(cancer|mutation).