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.

Key concepts

Understanding Recessive Disorders

Recessive disorders occur when both copies of a gene in an individual are altered or mutated. Each parent passes one copy of a gene to their offspring. For a recessive disorder to be present, a child must inherit a defective gene from both parents. This is why recessive disorders often "hide" in families and might not appear for several generations.

• Both parents must be carriers of the mutated gene for the child to manifest the disorder.
• If only one parent is a carrier, the child is a carrier too but does not show symptoms.
• It is possible for a person to be a carrier without knowing, which can complicate genetic counseling.

What is an Autosomal Disorder?

An autosomal disorder relates to genes that are located on the autosomes. Autosomes are the 22 pairs of chromosomes that are not involved in determining sex. This means both males and females can be affected equally by autosomal disorders.

• These disorders can be either dominant or recessive, depending on how they manifest.
• Recessive autosomal disorders require two copies of the mutated gene for symptoms to develop.
• They often play a significant role in genetic inheritance patterns observed in families worldwide.

Explaining Carrier Probability

Carrier probability is the likelihood that an individual carries one copy of a recessive gene mutation, even if they do not exhibit the disorder. Understanding carrier probability is crucial for assessing risk in potential offspring.

• If both parents are carriers, there's a 25% chance their child will have the disorder.
• The child has a 50% likelihood of being a carrier, inheriting the gene from only one parent.
• Carrier screening tests are available for many genetic disorders to help potential parents make informed decisions.

Genetic Probability Calculations Made Easy

Calculating genetic probabilities helps predict the likelihood of genetic trait inheritance in offspring. Let's walk through some basics.

• To find the probability of a child having a disorder, multiply the probabilities of each parent being a carrier.
• If both parents are carriers, the chance of their child having the disorder is 0.25 or 25%.
• For example, if each parent has a 2% probability of being a carrier, the calculation would be: \(0.02 \times 0.02 = 0.0004\), meaning a 0.04% probability that both are carriers.
• Then, multiply this probability by the 25% chance that both carrier parents pass the gene: \(0.0004 \times 0.25 = 0.0001\), resulting in a 0.01% chance.

These calculations aid genetic counselors and individuals in understanding genetic risks.