Your first cousin died of tay-sachs disease (autosomal recessive, incidence 0.09%). you are not affected, nor is anyone else in your extended family. what is the chance that you are a carrier?

25%

   Starting from my First cousin family, I know for sure that the Uncle is is a carrier (Aa) and he must have married a wife who is also a carrier (Aa) and that is how they got an affected son. Thus, this leads to the fact that either both of my grandparents are carriers (Aa x Aa) or only one of them is a carrier (Aa x AA). As a result, the chances that my mom (who is related to the uncle who has a defected child) is a carrier is either (2/3 or 1/2) depending if my grandparents genotype, respectively. Thus, if my mom chances of being a carrier is 1/2 then my chance of being a carrier is 1/4. (given that my dad is not a carrier b/c CF is a rare disease) However, if my mom chance of being a carrier is 2/3 then my chance of being a carrier is (2/3)x(1/2)=(1/3) As a result, I could either be 1/4 or 1/3. But since the answer only provide the choice of 1/4 and not 1/3. This leave 25% is the correct answer.