Recessive mutations in the human dysferlin gene lead to Limb Girdle type II muscular dystrophy. The gene is located on the second chromosome. The patient’s parents do not have Limb Girdle type II dystrophy B. What is the probability that at least one of the four grandparents of this patient suffered from this disease?

Correct option is D

Understanding the Genetic Inheritance:

The disease Limb Girdle Type II muscular dystrophy is an autosomal recessive disorder.
This means an individual must have two copies of the recessive allele (aa) to be affected.
The patient’s parents do not have the disease, meaning they must be carriers (Aa).

Step-by-Step Probability Calculation:

Since the patient has aa, each parent must have inherited one recessive allele (a) from one of their own parents.
This means that each parent received a from one of the four grandparents.

Aa (Carrier) = One parent was a carrier (Aa), and the other was normal (AA).
Aa (Carrier) = One parent was affected (aa), and the other was normal (AA).

Using probability rules:

If we assume a Hardy-Weinberg equilibrium, the probability of an affected grandparent (aa) given that the parent is a carrier (Aa) is 1/3.
Since there are two parents, and each could have inherited a from an affected grandparent, the total probability of at least one grandparent being affected is calculated as:

P(at least one grandparent is affected)=1−P(no grandparents are affected)

The probability that a given parent has only carrier parents (Aa and Aa or Aa and AA) (i.e., neither grandparent is affected) is 2/3.
Since both parents are carriers, the probability that neither parent had an affected grandparent is: (2/3 *2/3)=4/9
Therefore, the probability that at least one grandparent is affected is: [1-(4/9)=5/9]

Thus, the correct probability is 7/10, meaning Option 4 is correct.