Genetics Probability: Calculating Child Blood Group Genotype

This problem requires calculating the probability of a child inheriting a specific genotype for both ABO and Rh blood groups from parents with known genotypes.

ABO Blood Group Probability

The parents' ABO genotypes are AO (from the man) and BO (from the woman).

We can use a Punnett square to determine the possible ABO genotypes of the child:

The possible genotypes are AB, AO, BO, and OO. Each genotype has an equal probability of $\frac{1}{4}$.

The probability of the child having the OO genotype is $ P(\text{OO ABO}) = \frac{1}{4} $.

Rh Blood Group Probability

The parents' Rh genotypes are both $+-$ (heterozygous). Let's represent the alleles as R (positive) and r (negative). So, both parents are Rr.

We use another Punnett square for the Rh factor:

The possible Rh genotypes are RR, Rr, and rr. The probabilities are:

• RR: $\frac{1}{4}$
• Rr: $\frac{2}{4} = \frac{1}{2}$
• rr: $\frac{1}{4}$

The question asks for a child with genotype OO$^{+-}$. This means the child needs the OO ABO genotype and the Rh$^{+-}$ genotype. The Rh$^{+-}$ notation indicates heterozygosity for the Rh factor, which corresponds to the Rr genotype.

The probability of the child having the Rr (Rh$^{+-}$) genotype is $ P(\text{Rr Rh}) = \frac{1}{2} $.

Combined Probability

To find the total probability of the child having the OO$^{+-}$ genotype (meaning OO for ABO and Rr for Rh), we multiply the individual probabilities:

$ P(\text{Child Genotype OO}^{+-}) = P(\text{OO ABO}) \times P(\text{Rr Rh}) $

$ P(\text{Child Genotype OO}^{+-}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} $