Question

1. based on the information in this table, which man could not be the father of the baby? justify your answer with a punnett square.

name	blood type
baby	type b
the postman	type o
the ups driver	type ab
the waiter	type a
the cable guy	type b

Explanation:

Step1: Define blood type genotypes

Blood type A can be $I^A I^A$ or $I^A i$; type B is $I^B I^B$ or $I^B i$; type AB is $I^A I^B$; type O is $ii$. The baby has type B, so their genotype is either $I^B I^B$ or $I^B i$.

Step2: Analyze Postman (type O) cross

Mother (A: $I^A i$, only possible to pass $i$ for baby to get B) × Postman (O: $ii$)
Punnett square:
| | $I^A$ | $i$ |
|---|---|---|
| $i$ | $I^A i$ (A) | $ii$ (O) |
| $i$ | $I^A i$ (A) | $ii$ (O) |

Step3: Analyze other men's potential

- UPS driver (AB: $I^A I^B$) × Mother (A: $I^A i$): Can produce $I^B i$ (B) baby.
- Waiter (A: $I^A i$) × Mother (A: $I^A i$): Cannot produce B, but wait—wait, no: Mother must be $I^A i$, baby is $I^B i$, so waiter (A) can't give $I^B$, but wait no: Wait, baby is B, so needs $I^B$ from father. Waiter (A) has no $I^B$, but Postman (O) also has no $I^B$. Wait, correction: Baby is B, so must get $I^B$ from father. Postman (O) has only $i$, waiter (A) has $I^A$ or $i$. Wait, but mother is A, so she can only give $I^A$ or $i$. Baby is B, so must have $I^B$ from father. So any father without $I^B$ can't be father. But Postman (O) has no $I^B$, waiter (A) has no $I^B$. Wait, but wait: Baby's genotype is $I^B i$, so $i$ from mother, $I^B$ from father. So father must have $I^B$. So Postman (O: $ii$) can't give $I^B$, waiter (A: $I^A I^A$ or $I^A i$) can't give $I^B$. But wait, let's check Postman first:
Postman (O) × Mother (A: $I^A i$) can only have A or O babies, no B. Waiter (A: $I^A i$) × Mother (A: $I^A i$) can only have A or O babies, no B. But wait, the question is which could NOT be father. Wait, no: Wait, baby is B, so must have $I^B$ allele. So father must have $I^B$. So Postman (O) has no $I^B$, waiter (A) has no $I^B$. But wait, maybe mother is $I^A i$, baby is $I^B i$, so father must give $I^B$. So only UPS driver (AB) and Cable guy (B) have $I^B$. So Postman and Waiter can't be fathers? But no, wait, let's recheck:
Wait, baby is type B, so possible genotypes: $I^B I^B$ or $I^B i$. If baby is $I^B I^B$, then mother must give $I^B$, but mother is type A, which can't give $I^B$. So baby must be $I^B i$, so $i$ from mother, $I^B$ from father. So father must have $I^B$ allele. So Postman (O: $ii$) has no $I^B$, so can't give $I^B$. Waiter (A: $I^A I^A$ or $I^A i$) has no $I^B$, so can't give $I^B$. But wait, the question says "which man could not be the father". Wait, maybe I made a mistake. Wait, let's do Punnett square for Postman:
Mother (A: $I^A i$) × Postman (O: $ii$):
All offspring are $I^A i$ (A) or $ii$ (O). No B possible.
Waiter (A: $I^A i$) × Mother (A: $I^A i$):
Offspring: $I^A I^A$ (A), $I^A i$ (A), $ii$ (O). No B possible.
But wait, the question is which could NOT be father. But maybe the mother is $I^A I^A$? Then baby can't be B at all, but baby is B, so mother must be $I^A i$. So Postman and Waiter can't be fathers? But the question says "which man could not be the father". Wait, maybe I misread. Wait, the baby is type B, so father must have $I^B$. So Postman (O) has no $I^B$, so he can't be the father. Waiter (A) also has no $I^B$, but maybe the question considers that? Wait, no, let's check again:
Wait, type A can be $I^A I^A$ or $I^A i$. Type B can be $I^B I^B$ or $I^B i$. Type AB is $I^A I^B$, type O is $ii$.
Baby is type B, so must have at least one $I^B$ allele. Mother is type A, so she can only pass $I^A$ or $i$. Therefore, the $I^B$ allele must come from the father. So any father who does not have an $I^B$ allele cannot be the father.
- Postman (type O): genotype $ii$, no $I^B$ allele.
- UPS driver (type AB): genotype $I^A I^B$, has $I^B$ allele.
- Waiter (type A): genotype $I^A I^A$ or $I^A i$, no $I^B$ allele.
- Cable guy (type B): genotype $I^B I^B$ or $I^B i$, has $I^B$ allele.
But wait, the question says "which man could not be the father". Maybe the answer is the Postman and the Waiter? But let's check the Punnett square for the Postman:

Step4: Confirm Postman's impossibility

Mother (A: $I^A i$) × Postman (O: $ii$)
Punnett square:
| | $I^A$ | $i$ |
|---|---|---|
| $i$ | $I^A i$ (Type A) | $ii$ (Type O) |
| $i$ | $I^A i$ (Type A) | $ii$ (Type O) |
No possible Type B offspring.

Step5: Confirm Waiter's impossibility

Mother (A: $I^A i$) × Waiter (A: $I^A i$)
Punnett square:
| | $I^A$ | $i$ |
|---|---|---|
| $I^A$ | $I^A I^A$ (Type A) | $I^A i$ (Type A) |
| $i$ | $I^A i$ (Type A) | $ii$ (Type O) |
No possible Type B offspring.
But wait, the question says "which man could not be the father". Maybe the answer is the Postman and the Waiter? But let's recheck: the baby is Type B, so must have $I^B$ from father. So any father without $I^B$ can't be father. So Postman (O) and Waiter (A) can't be fathers. But maybe the question expects the Postman as the answer? Wait, no, both can't be. But let's see: the mother is Type A, so she can't give $I^B$, so baby's $I^B$ must come from father. So father must have $I^B$. So UPS driver (AB) and Cable guy (B) have $I^B$, so they can be fathers. Postman (O) and Waiter (A) don't have $I^B$, so they can't be fathers. But maybe the question is asking for one? Wait, no, let's check again.
Wait, maybe the mother is $I^A I^A$? Then baby can't be B at all, but baby is B, so mother must be $I^A i$. So baby is $I^B i$, so $i$ from mother, $I^B$ from father. So father must have $I^B$. So Postman (O) has no $I^B$, so can't be father. Waiter (A) has no $I^B$, so can't be father. But maybe the question has a typo? No, let's read again: "which man could not be the father". Maybe multiple, but let's present the Postman first, as his case is clearer.
Wait, no, both Postman and Waiter can't be fathers. But let's confirm:
If father is Postman (O), baby can only be A or O.
If father is Waiter (A), baby can only be A or O.
If father is UPS driver (AB), baby can be A, B, AB.
If father is Cable guy (B), baby can be A, B, AB, O.
So both Postman and Waiter can't be fathers. But maybe the question expects the Postman as the answer? Wait, no, let's check the Punnett square for Postman:

Answer:

The postman (Type O) and the waiter (Type A) could not be the father of the baby.

For the postman (genotype $ii$): When crossed with the mother (Type A, genotype $I^A i$), the only possible offspring blood types are Type A ($I^A i$) and Type O ($ii$), as shown in the Punnett square below, so a Type B baby is impossible.

	$I^A$	$i$
$i$	$I^A i$ (Type A)	$ii$ (Type O)

For the waiter (Type A, genotype $I^A i$): When crossed with the mother (Type A, genotype $I^A i$), the only possible offspring blood types are Type A ($I^A I^A$, $I^A i$) and Type O ($ii$), so a Type B baby is impossible.

	$I^A$	$i$
$i$	$I^A i$ (Type A)	$ii$ (Type O)

The most definitive answer is the postman, as his Type O genotype can never contribute the $I^B$ allele required for the baby's Type B blood.