Tay-Sachs. Tay-Sachs is a metabolic disorder that is inherited as an autosomal recessive trait. Both recessive alleles are necessary for expression of the disease. Therefore, when each parent is a carrier, there is a one in four chance of transmitting the genetic disorder to each offspring.

(a) Let X represent the number of offspring affected in three consecutive conceptions from Tay-Sachs carrier parents. Is X a binomial random variable? Explain your response.

(b) A carrier couple is unaware of their carrier state. Let X represent the number of children conceived before an affected offspring is encountered. Is X a binomial random variable? Explain.