Jerry is six years old.His sister Hanah has the autosomal recessive condition neuronal ceroid lipofuscinosis that affects learning and coordination.Their parents are healthy.The probability that Jerry is a homozygote for the wild type allele of the gene that causes the condition is
2-12-2013
A)1/8.
B)1/4.
C)1/3.
D)2/3.

Question

Quizplus · Accepted Answer

Since the parents are healthy, we know that they are both carriers of the gene for neuronal ceroid lipofuscinosis. This means that each parent has one wild type allele and one mutant allele.

When the parents have children, there are four possible combinations of alleles that the child can inherit:

1. Wild type allele from the mother, wild type allele from the father 
2. Wild type allele from the mother, mutant allele from the father 
3. Mutant allele from the mother, wild type allele from the father 
4. Mutant allele from the mother, mutant allele from the father

Of these four possible combinations, we are interested in knowing the probability that Jerry is a homozygote for the wild type allele. This means that Jerry would have had to inherit a wild type allele from both his mother and his father.

To calculate this probability, we need to consider the frequency of the wild type allele in the population. Since the gene is autosomal and there are only two alleles (wild type and mutant), the frequency of the wild type allele is simply the complement of the frequency of the mutant allele.

Let's use q to represent the frequency of the mutant allele. Since the parents are carriers, we know that each of them has a 1/2 chance of passing on the mutant allele to their child. Therefore, the probability of a child inheriting the mutant allele from both parents is (1/2) * (1/2) = 1/4.

This means that the frequency of the genotype mutant/mutant is q^2 = 1/4. Since there are only two possible genotypes (wild type/wild type or wild type/mutant), the frequency of the wild type/wild type genotype must be 1 - 1/4 = 3/4.

Therefore, the probability that Jerry is a homozygote for the wild type allele is (3/4)^2 = 9/16, which simplifies to 1/4.

Jerry Is Six Years Old