Hemochromatosis is an inherited disease caused by a recessive allele. If a woman and her husband, who are both carriers, have three children, what is the probability of each of the following?
a. All three children are of normal phenotype
b. One or more of the three children have the disease
c. All three children have the disease
d. At least one child is phenotypically normal

Verified step by step guidance

1. Step 1: Understand the genetic inheritance pattern. Hemochromatosis is caused by a recessive allele, meaning a person must inherit two copies of the recessive allele (one from each parent) to express the disease phenotype. Carriers have one dominant allele and one recessive allele, so they do not express the disease phenotype.
2. Step 2: Determine the genotype of the parents. Since both the woman and her husband are carriers, their genotype is heterozygous, represented as 'Hh' where 'H' is the dominant normal allele and 'h' is the recessive allele causing the disease.
3. Step 3: Use a Punnett square to calculate the probability of each genotype for their children. The possible combinations are: HH (normal phenotype), Hh (carrier, normal phenotype), and hh (disease phenotype). The probabilities are: 25% HH, 50% Hh, and 25% hh.
4. Step 4: Calculate the probability for each scenario using the genotype probabilities. For example, the probability that all three children are of normal phenotype (either HH or Hh) is calculated by considering the probability of each child being normal and multiplying these probabilities together.
5. Step 5: Use complementary probability for scenarios involving 'at least one' or 'one or more'. For instance, to find the probability that one or more children have the disease, calculate the probability that none have the disease and subtract from 1. Similarly, for at least one child being phenotypically normal, calculate the probability that all have the disease and subtract from 1.

Key Concepts

Genetic Inheritance

Genetic inheritance refers to the process by which genes and traits are passed from parents to offspring. In the context of recessive alleles, a trait or disease manifests only when an individual inherits two copies of the recessive allele, one from each parent. Carriers have one recessive allele but do not exhibit the trait, making understanding inheritance patterns crucial for predicting offspring phenotypes.

Punnett Square

A Punnett Square is a diagram used to predict the genotypes of offspring from parental alleles. It helps visualize how alleles combine during fertilization, showing the probability of inheriting specific traits. For two carrier parents, the Punnett Square reveals a 25% chance of offspring being affected, 50% chance of being carriers, and 25% chance of being unaffected.

Probability in Genetics

Probability in genetics involves calculating the likelihood of specific genetic outcomes based on allele combinations. For multiple offspring, probabilities are multiplied across events. For example, the probability of all three children being phenotypically normal involves calculating the chance for each child and multiplying these probabilities, considering the inheritance pattern of recessive alleles.