Blue eyes are recessive to any other color Both parents have

Blue eyes are recessive to any other color. Both parents have brown eyes, but each have a blue-eyed father. What is the probability that at least one of their three children is blue-eyed? Hint: sometime it is easier to calculate the P of the alternate event

Solution

Given that all parents have brown eyes and blue eyes are recessive and each have a blue eyed father. Means, both the paretns are heterozygous for the brown allele and is a dominant character.

Assuming that the gene coding for brown eyes is B and the gene coding for blue eyes if b; and B is dominant over b. The genotypes of both the paretns is, Bb. Cross between them will have the progeny with the following genotypes.

Bb* Bb ---> B_ (75% Brown eyes), bb (25% blue eyes)

Thus, the probability of having at least one children blue-eyed is = 1- the probability of having all brown-eyed children = 1 - (3/4)^3 = 1 - 27/64 = 37/64