Question

1. a person has type b blood. what are all the possible blood types of his parents. show the crosses to prove your answer.

Explanation:

Step1: Recall blood type genetics

Blood types are determined by alleles: $I^A$, $I^B$ (codominant), and $i$ (recessive). Type B blood has two possible genotypes: $I^BI^B$ or $I^Bi$. We need to find all parental crosses that can produce these genotypes.

Step2: Cross 1: $I^B$ parent + $I^B$ parent

Parents: $I^BI^B$ x $I^BI^B$
Offspring genotypes: $I^BI^B$ (100% type B)

$$\begin{array}{c|c} & I^B \\ \hline I^B & I^BI^B \\ \end{array}$$

Step3: Cross 2: $I^B$ parent + $I^Bi$ parent

Parents: $I^BI^B$ x $I^Bi$
Offspring genotypes: $I^BI^B$, $I^Bi$ (100% type B)

$$\begin{array}{c|cc} & I^B & i \\ \hline I^B & I^BI^B & I^Bi \\ \end{array}$$

Step4: Cross 3: $I^Bi$ parent + $I^Bi$ parent

Parents: $I^Bi$ x $I^Bi$
Offspring genotypes: $I^BI^B$ (25%), $I^Bi$ (50%), $ii$ (25%) → produces type B offspring

$$\begin{array}{c|cc} & I^B & i \\ \hline I^B & I^BI^B & I^Bi \\ i & I^Bi & ii \\ \end{array}$$

Step5: Cross 4: $I^B$ parent + $ii$ parent

Parents: $I^BI^B$ x $ii$
Offspring genotypes: $I^Bi$ (100% type B)

$$\begin{array}{c|cc} & i & i \\ \hline I^B & I^Bi & I^Bi \\ \end{array}$$

Step6: Cross 5: $I^Bi$ parent + $ii$ parent

Parents: $I^Bi$ x $ii$
Offspring genotypes: $I^Bi$ (50% type B), $ii$ (50% type O) → produces type B offspring

$$\begin{array}{c|cc} & i & i \\ \hline I^B & I^Bi & I^Bi \\ i & ii & ii \\ \end{array}$$

Step7: Cross 6: $I^B$ parent + $I^Ai$ parent

Parents: $I^BI^B$ x $I^Ai$
Offspring genotypes: $I^AI^B$ (type AB), $I^Bi$ (type B) → produces type B offspring

$$\begin{array}{c|cc} & I^A & i \\ \hline I^B & I^AI^B & I^Bi \\ \end{array}$$

Step8: Cross 7: $I^Bi$ parent + $I^Ai$ parent

Parents: $I^Bi$ x $I^Ai$
Offspring genotypes: $I^AI^B$ (AB), $I^Ai$ (A), $I^Bi$ (B), $ii$ (O) → produces type B offspring

$$\begin{array}{c|cc} & I^A & i \\ \hline I^B & I^AI^B & I^Bi \\ i & I^Ai & ii \\ \end{array}$$

Step9: Cross 8: $I^B$ parent + $I^AI^B$ parent

Parents: $I^BI^B$ x $I^AI^B$
Offspring genotypes: $I^AI^B$ (AB), $I^BI^B$ (B) → produces type B offspring

$$\begin{array}{c|cc} & I^A & I^B \\ \hline I^B & I^AI^B & I^BI^B \\ \end{array}$$

Step10: Cross 9: $I^Bi$ parent + $I^AI^B$ parent

Parents: $I^Bi$ x $I^AI^B$
Offspring genotypes: $I^AI^B$ (AB), $I^AI^i$ (A), $I^BI^B$ (B), $I^Bi$ (B) → produces type B offspring

$$\begin{array}{c|cc} & I^A & I^B \\ \hline I^B & I^AI^B & I^BI^B \\ i & I^Ai & I^Bi \\ \end{array}$$

Answer:

All possible parental blood type pairs (order does not matter) are:

1. Type B and Type B
2. Type B and Type O
3. Type B and Type A
4. Type B and Type AB
5. Type A and Type O (only when the A parent is $I^Ai$)
6. Type AB and Type O
7. Type AB and Type A