Muscular dystrophy i an incurable muscle-wasting disease. The most common and se

Question

Muscular dystrophy i an incurable muscle-wasting disease. The most common and serious type, called DMD, is caused by a sex-linked recessive mutation. Specifically, women can be carriers but do not get the disease; a son of a carrier has probability 0.5 of having DMD; a daughter has probability 0.5 of being a carrier. As many as one-third of DMD cases, however, are due to spontaneous mutations in sons of mothers who are not carriers. Toni has one son, who has DMD. In the absence of other information, the probability is 1/3 that the son is the victim of a spontaneous mutation and 2/3 that Toni is a carrier. There is a screening test called the CK test that is positive with probability 0.6 if a woman is a carrier and with probability 0.05 if she is not. Toni's CK test is positive. What is the probability that she is a carrier? (Round your answer to two decimal places.)

Explanation / Answer

Solution:

P(Son gets DMD|Mom carrier) = 0.5

P(Daughter Carrier of DMD|Mom carrier) = 0.5

P(Son has DMD|Mom not carrier) = 1/3 = 0.3333

Toni has one son who has DMD
P(CK test Postive|Mom is carrier) = 0.6

P(CK test negative|Mom is not carrier) = 0.05

P(Toni carrier| test positive) = ?

After I wrote all this down, and I began constructing the tree, I realized that I did not need much of the information that was given.

P(Toni carrier | test positive) = [2/3(0.6)] / [2/3(0.6)+1/3(0.05)] = 0.96

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