Question

Achondroplasia is a common form of dwarfism caused by an autosomal dominant mutation in the fibroblast growth factor receptor 3 (FGFR3) gene. Two copies of the mutant gene are invariably fatal before or shortly after birth. If a person with achondroplasia marries a person of normal height, what is the probability that both their first child and second child will have achondroplasia?

Answer 1

If a person with achondroplasia marries a person of normal height, the probability that both their first child and second child will have achondroplasia is 25%. The chance is influenced by the genotypes of the parents and the fact that achondroplasia is an autosomal dominant disorder.

Step-by-step explanation:

If a person with achondroplasia marries a person of normal height, the probability that both their first child and second child will have achondroplasia depends on the genotypes of the parents. Achondroplasia is an autosomal dominant disorder, which means that an individual only needs one copy of the mutant gene to have the condition. In this case, the person with achondroplasia would be heterozygous, having one normal copy of the FGFR3 gene and one mutant copy. The person of normal height would be homozygous for the normal allele.

When a heterozygous parent with achondroplasia has a child with a homozygous normal parent, the possible genotypes of the offspring are heterozygous (one mutant allele and one normal allele) or homozygous normal (two normal alleles). The probability of having a child with achondroplasia is 50%, while the probability of having a child without achondroplasia is also 50%.

Therefore, the probability that both their first child and second child will have achondroplasia is 25% (0.5 * 0.5 = 0.25 or 25%).

Answer 2

1/4

Step-by-step explanation:

Achondroplasia is caused by an autosomal dominant mutation. Two copies of the mutant allele are fatal.

The possible genotypes and phenotypes for this gene are:

• AA: lethal
• Aa: achondroplasia
• aa: normal height

If a person with achondroplasia marries a person of normal height: the corss is Aa x aa.

Their children can have the following genotypes:

• 1/2 Aa (achondroplasia)
• 1/2 aa (normal)

Each time the couple has children, the gametes that combine do so randomly and independently. According to the rule of multiplication, the probability of occurrence of two independent events can be calculated as the multiplication of the probability of each one.

Therefore, the probability of having the first two children with achondroplasia will be 1/2 × 1/2 = 1/4.