Problem 4.5. Sickle cell anemia is a genetic blood disorder. Two alleles are imp

Question

Problem 4.5. Sickle cell anemia is a genetic blood disorder. Two alleles are important for the inheritance of sickle cell anemia: the sickle allele (S) and the normal adult haemoglobin allele (A) (see [:321). Individuals with two normal A alleles (AA) have normal hemoglobin. Those with two mutant S alleles (SS) develop sickle cell anemia. Those who are heterozygous for the sickle cell allele (AS) produce both normal and abnormal hemoglobin. The heterozygotes are said to have the sickle cell trait. Individuals with the sickle cell trait or anemia are more resistant to malaria. Consider a population in which 20% of the individuals have a sickle cell allele. (a) Assume that in a certain region, the probability of dying of malaria is 15% for individuals that do not have the sickle cell allele, and 2.5% for individuals with a sickle cell allele. What is the probability of dying of malaria iii this region? (b) If an individual from this population dies from malaria, what is the probability that this individual had a sickle cell allele?

Explanation / Answer

a)

P(die) = P(sickle) P(die|sickle) + P(no sickle) P(die|no sickle)

= 0.20(0.025) + (1-0.20)(0.15)

= 0.125 [ANSWER]

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b)

P(die|sickle) = P(die and sickle)/P(die)

As

P(die and sickle) = P(sickle) P(die|sickle) = 0.20(0.025) = 0.005

Then

P(die|sickle) = 0.005/0.125 = 0.04 [ANSWER]

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