Question

Genetics There are many married couples in which the husband and wife both carry a gene for cystic fibrosis but don’t have the disease themselves. Suppose we select one of these couples at random. According to the laws of genetics, the probability that their first child will develop cystic fibrosis is $0.25.$

a. Interpret this probability as a long-run relative frequency.

b. If researchers randomly select $4$such couples, is one of these couples guaranteed to have a first child who develops cystic fibrosis? Explain your answer.

Short answer

a) We find that the firstborn kid will get cystic fibrosis in about $25\%$of them.

b) The sample size must be quite large in order for the probability to be closely reflected in the sample.

Step-by-step solution

Part (a) Step 1: Given information

We have to interpret this probability as a long-run relative frequency.

Part (a) Step 2: Explanation

When we look at numerous couples when both the husband and wife have this gene, we find that the firstborn kid will get cystic fibrosis in about $25\%$of them.

Part (b) Step 1: Given information

We have to explain the answer about first child who develops cystic fibrosis.

Part (b) Step 2: Explanation

• If the family has four children, the sample size is four, which is relatively tiny.

• The sample size must be quite large in order for the probability to be closely reflected in the sample.