Calculating the Probability of a Blue-Eyed Redhead Child

Explanation:

The Genetics Behind the Probability:

The question is asking about the probability of a couple with given genotypes having a child with a specific set of traits: blue eyes (bb) and red hair (Rr). Both parents are heterozygous for brown eyes (Bb), with one parent being a blonde (rr) and the other a redhead (Rr).

Eye Color Probability:

Since both parents carry a recessive blue eye allele (b), the probability of having a child with blue eyes (bb) is 1/4. This is because there is a 25% chance for the child to inherit the recessive blue eye allele from each parent.

Hair Color Probability:

The redhead allele (R) is dominant to the blonde hair allele (r). With one parent being a redhead (Rr) and the other a blonde (rr), the probability of having a child with red hair (at least one R allele) is 1/2. The child needs to inherit the dominant redhead allele from the redhead parent, who has a 50% chance of passing it on.

Overall Probability Calculation:

By multiplying the probabilities of each independent event (blue eyes and red hair), we get: Probability(blue eyes) × Probability(red hair) = 1/4 × 1/2 = 1/8. Therefore, the probability of their next child being a blue-eyed redhead is 12.5% or 1/8.