Question

Phenylkeptonuria (PKU) is a disease that results from a recessive gene and 1/20,000 in the population know to be carriers. Two unaffected parents produce a child with PKU. (a) What is the probability that their next child will have PKU? (b) They want to have a big family and decide to have 4 more children. What is the probability that at least one child out of next 4 children will not show PKU?

Answer #1

Probability of the father carrying the recessive gene = 1/20000

Probability of the father passing down the recessive gene = 1/2 x 1/20000 = 1/40000

Probability of the mother carrying the recessive gene = 1/20000

Probability of the mother passing down the recessive gene = 1/2 x 1/20000 = 1/40000

a. Probability of the offspring to carry both recessive gene =
1/40000 x 1/40000 = 1/(16 x 10^{8})

b. Probability of atleast one in four offsprings carrying the
disease = 4 x 1/40000 x 1/40000 = 1/(4 x 10^{8})

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