Cystic fibrosis is inherited as an autosomal recessive disorder. Two parents without cystic fibrosis have 2 children with cystic fibrosis and 3 children without. The parents come to you for genetic counseling. If the parents have 2 more children, what is the probability that both children will hve the same phenotype (i.e. both have cystic fibrosis or both don't have cystic fibrosis)?

Ans.

Cystic fibrosis is inherited as an Autosomal Recessive disorder.

Lets denote the Alleles with C ( for Dominant Allele) and c (for Recessive Allele)

So,
CC = not Affected
Cc = not Affected
cc = Affected with Cystic fibrosis

So, 2 parents without Cystic fibrosis giving Birth to Children with Cystic fibrosis
means Parents were Heterozygous (Cc)

Now,
Parents with Cc, gives gametes = C and c
So,
C X C = CC
C X c = Cc
c X C = Cc
c X c = CC
now,
Probability of Child with Cystic fibrosis = 1/4
Probability of Child without Cystic fibrosis = 3/4

Answer :
Probability of 2 Children with Cystic fibrosis = 1/4 * 1/4 = 1/16

Probability of 2 Children without Cystic fibrosis = 3/4 * 3/4 = 9/16