Typically we talk about blood types as B-positive or AB-negative and so forth. The

positive and negative part of the blood type is determined by a completely separate gene (the
Rh locus). The ABO locus and the Rh locus are inherited independently, like pea shape and
pea color. The positive phenotype is dominant to the negative phenotype. A father has
genotype IA IO Rh+Rh– and a mother has genotype IA IB Rh+Rh–.
a. What are the phenotypes of these parents?
b. What is the probability that their only child will have phenotype B-positive?

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In order to determine the phenotypes of the parents in this scenario, we need to understand how blood types and the Rh factor inheritance work.

a. Phenotypes of the Parents:
- Father's genotype: IA IO Rh+ Rh–
- Mother's genotype: IA IB Rh+ Rh–

To determine the phenotypes, let's break down the genotypes:

Father's genotype: IA IO Rh+ Rh–
The father has blood type A (genotype IA IO). The IA allele gives him the A antigen, while the IO allele means he does not have the B antigen. So, his blood type is A.

The father is Rh positive (Rh+), indicated by the presence of the Rh antigen.

Mother's genotype: IA IB Rh+ Rh–
The mother has blood type AB (genotype IA IB). The IA and IB alleles both provide antigens A and B, respectively. Therefore, her blood type is AB.

Similar to the father, the mother is Rh positive (Rh+).

Therefore, the phenotypes of the parents are:
- Father: A positive (A+)
- Mother: AB positive (AB+)

b. Probability of Child's Phenotype:
To determine the probability that their only child will have phenotype B positive (B+), we need to analyze the potential combinations of alleles from both parents using Punnett squares.

Father's genotype: IA IO Rh+ Rh–
Mother's genotype: IA IB Rh+ Rh–

Let's focus on the ABO locus for the blood type:

The possible alleles that each parent can pass on are as follows:
- Father: IA or IO
- Mother: IB or IA

Using this information, we can construct a Punnett square to determine the potential blood types of their child:

```
| IA | IO
---------------------
IB | AB | B
---------------------
IA | A | A
```

From this Punnett square, we see that the child has a 50% chance of inheriting the B allele from the mother and a 50% chance of inheriting the A allele from the father. Since the Rh factor inheritance is independent of the ABO locus, the child also has a 100% chance of inheriting the Rh+ allele from both parents.

Considering both the ABO locus and the Rh locus, the probability that their only child will have the phenotype B positive (B+) is 50%.

Please note that this explanation assumes basic Mendelian genetics and does not take into account other variables or genetic interactions that may affect blood type inheritance.