Final answer:
1. The probability of the father's sperm containing the PKU allele is 50%. 2. The probability of the mother's egg containing the PKU allele is 50%. 3. The probability of their next child having PKU is 25%. 4. The probability of their next child being heterozygous for the PKU gene is 50%.
Step-by-step explanation:
1. The probability that a sperm from the father will contain the PKU allele is 1/2 or 50%. Since the father is normal and does not have PKU, he must be heterozygous for the PKU gene (carrier) with one normal allele and one PKU allele. Therefore, there is a 50% chance that a sperm will carry the PKU allele.
2. The probability that an egg from the mother will contain the PKU allele is also 1/2 or 50%. Just like the father, the mother must also be heterozygous for the PKU gene (carrier) with one normal allele and one PKU allele. Therefore, there is a 50% chance that an egg will carry the PKU allele.
3. The probability that their next child will have PKU is 1/4 or 25%. For the child to have PKU, both the sperm and the egg must carry the PKU allele. Since the probability of each parent's gamete carrying the PKU allele is 1/2, the probability of both gametes carrying the PKU allele is 1/2 * 1/2 = 1/4.
4. The probability that their next child will be heterozygous for the PKU gene is 1/2 or 50%. This is because there are two possible ways for the child to be heterozygous - either the sperm carries the PKU allele and the egg carries the normal allele, or vice versa. Each of these possibilities has a 1/2 probability, so the overall probability is 1/2 + 1/2 = 1/2.