Question

Neither Tim nor Rhoda has Duchenne muscular dystrophy, but their firstborn son does. What is the probability that a second child will have the disease? What is the probability if the second child is a boy? A girl?

Answer 1

Answer:

There is a 25% chance that their second child has Duchenne Muscular Dystrophy. There is a 50% chance that their second child is a boy and 50% chance that their second child is a girl

Step-by-step explanation:

As neither Tim nor Rhonda have muscular dystrophy that suggests that it is a recessive trait and both the parents are carriers for the disease. The Punnett Square is a way of determining the probability of offspring having particular genetic traits of their parents.

Considering $A_{D}$ to be the recessive gene causing muscular dystrophy and $A$ to be the dominant gene preventing it, the attached Punnett Square can be made. Based on it, there is 1 combination (green square) out of 4 ($A_{D}A_{D}$) which will have both genes causing muscular dystrophy which will make it present in the offspring. That means there is a 25% chance that any child of Tim and Rhonda may have muscular dystrophy.

The probability of gender of their child can be determined in the same way. Considering females to have XX genes and males to have XY genes, the second attached Punnett Square can be made. From it, it can be seen that there is a 50% chance of Tim and Rhonda having either a boy (orange square) or a girl (blue square).