sickle cell anemia is a recessive condition. Two diploid parents, heterozygous for sickle cell anemia produce...

sickle cell anemia is a recessive condition. Two diploid parents, heterozygous for sickle cell anemia produce 5 offspring. What is the probability that the parents have 3 or more children with sickle cell anemia? Using binomial distribution.

Expert Solution

Sickle cell anemia is a recessive condition, hence requires two alleles.

Normal (S) > Sickle-cell (s)
Normal genotypes = SS, Ss, sS
Sickle-cell genotypes = ss

Genotypes of the parents: Ss

As per Mendelian Laws of Inheritance (Segregation, Independent Assortment, and Dominance):

Probability of having sickle-cell child = 1/4
Probability of having normal child = 3/4
Number of ways in which 3 kids can be selected from a group of 5 kids = ⁵C₃
Probability that the parents have 3 children with sickle cell anemia = ⁵C₃ (1/4)³ (3/4)² = 90/1024 = 8.789%
Number of ways in which 4 kids can be selected from a group of 5 kids = ⁵C₄
Probability that the parents have 4 children with sickle cell anemia = ⁵C₄ (1/4)⁴ (3/4)¹ = 15/1024 = 1.464%
Number of ways in which 5 kids can be selected from a group of 5 kids = ⁵C₅
Probability that the parents have 5 children with sickle cell anemia = ⁵C₅ (1/4)⁵ (3/4)⁰ = 1/1024 = .0976%

Probability that the parents have 3 or more children with sickle cell anemia = 106/1024 = 10.351%

gladiator answered 1 year ago

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