The accompanying pedigree shows the transmission of albinism (absence of skin pigment) in a human family.

The female I-1 and her mate, male I-2, had four children, one of whom has albinism. What is the probability that they could have had a total of four children with any other outcome except one child with albinism and three with normal pigmentation? 

Verified step by step guidance

1. Step 1: Understand the inheritance pattern of albinism. Albinism is typically inherited as an autosomal recessive trait, meaning that an individual must inherit two copies of the recessive allele (one from each parent) to express the condition. Individuals with one dominant allele and one recessive allele are carriers but do not express albinism.
2. Step 2: Determine the genotypes of the parents (I-1 and I-2). Since one of their children has albinism, both parents must be carriers of the recessive allele (heterozygous, Aa). This is because a child with albinism (aa) can only inherit a recessive allele from each parent.
3. Step 3: Use a Punnett square to calculate the probabilities of offspring genotypes. Cross the genotypes of the parents (Aa x Aa). The possible genotypes for their children are: AA (normal pigmentation, not a carrier), Aa (normal pigmentation, carrier), and aa (albinism). The probabilities are: 25% AA, 50% Aa, and 25% aa.
4. Step 4: Calculate the probability of having one child with albinism and three with normal pigmentation. This involves using the binomial probability formula: \( P = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \), where \( n \) is the total number of children, \( k \) is the number of children with albinism, \( p \) is the probability of albinism (0.25), and \( 1-p \) is the probability of normal pigmentation (0.75).
5. Step 5: Subtract the probability calculated in Step 4 from 1 to find the probability of any other outcome except one child with albinism and three with normal pigmentation. This accounts for all other combinations of children with albinism and normal pigmentation.

Key Concepts

Inheritance Patterns

Understanding inheritance patterns, particularly autosomal recessive traits like albinism, is crucial. Albinism typically requires two copies of the recessive allele for an individual to express the trait. Therefore, knowing the genotypes of the parents and how traits are passed down through generations helps in predicting the likelihood of offspring exhibiting specific traits.

Probability in Genetics

Probability in genetics involves calculating the likelihood of certain genetic outcomes based on parental genotypes. For example, if both parents are carriers of the albinism allele, the probability of having a child with albinism can be determined using a Punnett square, which visually represents the potential genetic combinations of the offspring.

Pedigree Analysis

Pedigree analysis is a tool used to trace the inheritance of traits through generations in a family. By examining a pedigree chart, one can identify patterns of inheritance, determine carrier status, and assess the probability of future offspring inheriting specific traits, such as albinism, based on the family history.