Genetics A gene is composed of two alleles, either dominant or recessive. Suppose that a husband and wife, who are both carriers of the sickle-cell anemia allele but do not have the disease, decide to have a child. Because both parents are carriers of the disease, each has one dominant normal-cell allele (S) and one recessive sickle-cell allele (s). Therefore, the genotype of each parent is Ss. Each parent contributes one allele to his or her offspring, with each allele being equally likely.


c. What is the probability that the offspring will not have sickle-cell anemia but will be a carrier? In other words, what is the probability that the offspring will have one dominant normal-cell allele and one recessive sickle-cell allele? Interpret this probability.

Verified step by step guidance

1. Step 1: Identify the possible alleles each parent can pass on. Since each parent has genotype Ss, they can pass on either the dominant allele S or the recessive allele s, each with probability 1/2.
2. Step 2: List all possible genotype combinations for the offspring by combining one allele from each parent. The possible genotypes are: SS, Ss, sS, and ss. Note that Ss and sS represent the same genotype (carrier).
3. Step 3: Calculate the probability for each genotype by multiplying the probabilities of each parent's allele contribution. For example, the probability of Ss is the probability that the father passes S (1/2) and the mother passes s (1/2), so \(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\).
4. Step 4: Since Ss and sS are the same genotype (carrier), add their probabilities together to find the total probability that the offspring is a carrier: \(P(\text{carrier}) = P(Ss) + P(sS)\).
5. Step 5: Interpret the result as the likelihood that the child will inherit one dominant normal allele and one recessive sickle-cell allele, meaning the child will be a carrier but will not have sickle-cell anemia.

Key Concepts

Mendelian Genetics and Alleles

Mendelian genetics explains how traits are inherited through alleles, which are different forms of a gene. Each individual has two alleles per gene, one from each parent. Dominant alleles mask the effect of recessive alleles, so a dominant allele will determine the trait if present. In this case, 'S' is dominant (normal) and 's' is recessive (sickle-cell).

Punnett Square and Probability of Genotypes

A Punnett square is a tool used to predict the probability of offspring genotypes based on parental alleles. Each parent contributes one allele randomly, so the combinations can be mapped to calculate probabilities. For two Ss parents, the possible offspring genotypes are SS, Ss, and ss, with probabilities derived from the square.

Carrier Status and Disease Expression

A carrier has one dominant and one recessive allele (Ss) and does not express the disease but can pass the recessive allele to offspring. The disease manifests only if the individual inherits two recessive alleles (ss). Understanding carrier probability helps assess genetic risk and informs genetic counseling.