b. (12 points) Sickle-cell anemia is an inher ited disease in which red blood ce
ID: 3061290 • Letter: B
Question
b. (12 points) Sickle-cell anemia is an inher ited disease in which red blood cells are misshapen and sticky. Sickle cells tend to form clumps in blood vessels, inhibiting for of blood. Humans have two genes for sickle-cell anemia, either of which may be S normal cells or s for sickl le cells. A person with two copies of the s gene will have sickle- cell anemia. A person with one s gene and one S gene will not have the disease, but will be a carrier, which means that the s gene may be transmitted to the person's offspring. If two carriers have a child, the probability is 0.25 that the child will have the disease, and 0.5 that the child will be a carrier. Outcomes among children are independent. Assume that a mother and father who are both carriers have two children. (i) What is the probability that neither child has the disease? (ii) What is the probability that both children are carriers? (ii) If neither child has the disease, what is the probability that both are carriers?Explanation / Answer
(i)P(neither child has the disease) =P(first des nt have)*P(second does not have) =(1-0.25)2 =0.5625
(ii)P(borth are carriers) =P(first is carrier)*P(second is carrier) =0.5*0.5 =0.25
(iii) P(both are carrier|neither has disease) =P(both are carrier)/P(neither has disease) =0.25/0.5625=0.4444
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