Question

Genetics Suppose a married man and woman both carry a gene for cystic fibrosis but don’t have the disease themselves. According to the laws of genetics, the probability that their first child will develop cystic fibrosis is $0.25$

(a) Explain what this probability means.

(b) Why doesn’t this probability say that if the couple has $4$ children, one of them is guaranteed to get cystic fibrosis?

Short answer

Part (a) The probability of a disease in the first child is $0.25$If they have a child, the child's survival chances are $25\%$

Part (b) If they have many children about $1/4$would have the disease.

Step-by-step solution

Part (a) Step 1. Given Information

The probability of a child obtaining cystic fibrosis for the first time $0.25$

Part (a) Step 2. Concept

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The probability of a chance outcome is its long-run relative frequency.

Part (a) Step 3. Explanation 

According to the probability indicated in the question, roughly $25\%$ of all married men and women who both possess the cystic fibrosis gene but do not have the disease develop cystic fibrosis in their children. As a result, the probability in the question has this meaning.

Part (b) Step 1. Explanation 

Because the probability does not state that if a couple has $4$ children, one of them would acquire cystic fibrosis, it is possible that if they have $4$ children, none of them will develop cystic fibrosis. We may also claim that none of the children will develop cystic fibrosis, but it is possible.