Your mother has albinism, which is a recessive trait. Your father has cystic fibrosis, which is also a recessive trait. You discover that your new father-in-law has albinism and cystic fibrosis. If neither you nor your spouse has either albinism or cystic fibrosis, what are the odds that your first child will have either albinism or cystic fibrosis, but not both?
A) 1/16
B) 3/8
C) 1/8
D) 1/4
E) 0

Question

Quizplus · Accepted Answer

Since albinism and cystic fibrosis are both recessive traits, you and your spouse are carriers of both genes. The probability of your child inheriting one of these conditions (but not both) is calculated by adding the probability of inheriting albinism without cystic fibrosis to the probability of inheriting cystic fibrosis without albinism. Each parent has a 1/2 chance of passing on the recessive gene for each condition. The probability for one condition (e.g., albinism) without the other (cystic fibrosis) is (1/2 * 1/2) * (1/2 * 1/2) = 1/16 for albinism without cystic fibrosis and 1/16 for cystic fibrosis without albinism. Adding these probabilities gives 1/16 + 1/16 = 1/8. However, this calculation overlooks the scenario where the child inherits one condition from one parent and the other condition from the other parent, which also has a probability of 1/16. Therefore, the total probability is 1/8 (for one condition without the other) + 1/16 (for inheriting one condition from one parent and the other condition from the other parent) = 3/16. The correct calculation for the probability of inheriting either condition but not both should consider the combinations of inheriting one condition from one parent and not the other condition from either parent, leading to a probability of 3/8 when correctly accounting for all possible combinations.

Your Mother Has Albinism, Which Is a Recessive Trait