Final answer:
The chance that you are a carrier of Tay-Sachs disease is 25% since it implies that one of your parents must be a carrier, giving you a 50% chance of also being a carrier.
Step-by-step explanation:
To answer the question of what the chance is that you are a carrier of Tay-Sachs disease, it's important to understand how genetics work in autosomal recessive conditions. Since your first cousin was affected by Tay-Sachs, it means that both of their parents (your aunt/uncle and their spouse) were carriers of the recessive gene. As Tay-Sachs is an autosomal recessive disorder, an individual must inherit two copies of the harmful allele to be affected by the disease. Carriers have one copy of the mutated gene, but do not show symptoms.
Inheriting Tay-Sachs disease requires receiving the recessive gene from both parents. Since you share one set of grandparents with your cousin, at least one of your parents must be a carrier. Therefore, the chances that you are also a carrier are not just the general population risk of 0.09%, but must be recalculated based on family genetics. Your parent, who is a sibling to your cousin's affected parent, has a 50% chance of being a carrier because one of their parents must have been a carrier. If your parent is a carrier, you then have a 50% chance of being a carrier yourself. The combined probability of both events happening is 25% (0.5 * 0.5 = 0.25 or 25%).
Therefore, the correct answer is d) 25%