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Chapter 5: Q 3. (page 294)

Genetics Suppose a married man and woman both carry a gene for cystic fibrosis but don鈥檛 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鈥檛 this probability say that if the couple has 4 children, one of them is guaranteed to get cystic fibrosis?

Short Answer

Expert verified

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

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

Step by step solution

01

Part (a) Step 1. Given Information

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

02

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.

03

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.

04

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.

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Most popular questions from this chapter

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