BRCA1 and BRCA2 are two genes in humans, mutations of which are associated with

Question

BRCA1 and BRCA2 are two genes in humans, mutations of which are associated with breast cancer. Of all females that carry mutations, 1/3 of them carry a mutation in the BRCA1 gene and 2/3 in the BRCA2 gene (suppose that nobody carries mutations in both genes). If the probability of developing cancer is 3/5 for women who carry a BRCA1 mutation and 1/5 for women who carry a BRCA2 mutation, what is the probability that a randomly chosen female who carries a mutation will develop breast cancer? (Enter your probability as a fraction.)

Explanation / Answer

In the problem a randomly chosen female who carries mutation can develop cancer either through BRCA1 gene or through BRCA2 gene.

Now, given that the probability of carring mutation in the BRCA1 Gene is 1/3.

So, P(BRCA1) = 1/3.

Similarly, from the problem P(BRCA2) = 2/3.

Also, the probability of developing cancer to women who carry a BRCA1 mutation is 3/5.

So, P(C|BRCA1) = 3/5.

Similarly, P(C|BRCA2) = 1/5.

So, from the theorem of total probability,

Probability of developing cancer to a randomly selected woman is

P(C) = P(C|BRCA1)*P(BRCA1) + P(C|BRCA2)*P(BRCA2) =  (3/5)*(1/3) + (1/5)*(2/3) = (3/15) + (2/15) = 5/15 = 1/3.

Hence, the probability of developing breast cancer to a randomly chosen female who carries a mutation is 1/3.

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.