Question

Assume that a recessive autosomal disorder occurs in 1 of 10,000 individuals (0.0001) in the general population and that in this population about 2 percent (0.02) of the individuals are carriers for the disorder. Estimate the probability of this disorder occurring in the offspring of a marriage between first cousins. Compare this probability to the population at large.

Short answer

Answer: The probability of the recessive autosomal disorder occurring in the offspring of a marriage between first cousins is 0.0001, which is the same as in the general population (1 in 10,000).

Step-by-step solution

Find the probability that one of the first cousins is a carrier

In the general population, 0.02 or 2% of individuals are carriers. Therefore, the probability that one of the first cousins is a carrier is equal to 0.02.

Find the probability that both first cousins are carriers

Since both cousins are part of the general population, we can assume that they have the same probability of being a carrier. To find the probability that both are carriers, we multiply the individual probabilities together: 0.02 * 0.02 = 0.0004.

Find the probability that their offspring inherits the disorder

If both parents are carriers, there is a 1 in 4 chance that their offspring will inherit the disorder. In probability terms, this is equal to 0.25 or 25%.

Find the probability of the disorder in the offspring of first cousins

To find the probability that an offspring of first cousins will have the disorder, multiply the probability that both parents are carriers (0.0004) by the probability that their offspring inherits the disorder (0.25): 0.0004 * 0.25 = 0.0001.

Compare the probability to the general population

The probability of the recessive autosomal disorder occurring in the offspring of a marriage between first cousins is 0.0001, which is the same as the percentage of individuals affected by the disorder in the general population (0.0001 or 1 in 10,000). So the probability of the disorder occurring in the offspring of first cousins is the same as in the general population.