Final answer:
The probability that a couple's first child will be a girl with dentinogenesis imperfecta, an autosomal dominant disorder, is 1/4. This is calculated by multiplying the probability of having a girl (1/2) with the probability of inheriting the condition (1/2).
Step-by-step explanation:
The question revolves around a genetic condition known as dentinogenesis imperfecta, which is an autosomal dominant disorder. This means that only one copy of the gene is required for an individual to express the phenotype associated with the disorder. To calculate the probability that the first child of the couple will be a girl with dentinogenesis imperfecta, two independent events need to be considered: the child being a girl and the child inheriting the condition.
The probability of the child being a girl is 1/2. Since the father has dentinogenesis imperfecta and the mother has normal teeth, the offspring has a 1/2 chance of inheriting the affected gene from the father if the gene for the condition is on one of the autosomes and not linked to the sex chromosomes. These two probabilities are independent, so they must be multiplied together to get the combined probability of both events occurring. The calculation is as follows: 1/2 (probability of being a girl) x 1/2 (probability of inheriting the disorder) = 1/4.
Therefore, the probability that their first child will be a girl with dentinogenesis imperfecta is 1/4, which corresponds to option A.