Tay-Sachs disease (infantile amaurotic idiocy) is a rare human disease in which toxic substances accumulate in nerve cells. The recessive allele responsible for the disease is inherited in a simple Mendelian pattern. For unknown reasons, the allele is more common in populations of Ashkenazi Jews of eastern Europe.

A woman is planning to marry her first cousin, but the couple discovers that their shared grandfather's sister died in infancy from Tay-Sachs disease. What is the probability that the cousins' first child will have Tah-Sachs disease, assuming that all people who marry into the family are homozygous normal?