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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

Sampling senators Refer to Exercise 50.

(a) Construct a Venn diagram that models the chance process using events R: is a Republican, and F: is female.

(b) Find P(R鈭�F) Interpret this value in context.

(c) Find P(Rc鈭�Fc) Interpret this value in context.

Who eats breakfast? Students in an urban school were curious about how many children regularly eat breakfast. They conducted a survey, asking, 鈥淒o you eat breakfast on a regular basis?鈥� All 595 students in the school responded to the survey. The resulting data are shown in the two-way table

below.7 Male Female Total Eats breakfast regularly 190110300 Doesn鈥檛 eat breakfast regularly 130165295Total320275595

(a) Who are the individuals? What variables are being measured?

(b) If we select a student from the school at random, what is the probability that we choose

  • a female?
  • someone who eats breakfast regularly?
  • a female who eats breakfast regularly?
  • a female or someone who eats breakfast

regularly?

Nickels falling over You may feel it鈥檚 obvious that the probability of a head tossing a coin is about12because the coin has two faces. Such opinions are not always correct. Stand a nickel on the edge on a hard, flat surface. Pound the surface with your hand so that the nickel falls over. Do this 25time, and record the results.

(a) What鈥檚 your estimate for the probability that the

coin falls heads up? Why?

(b) Explain how you could get an even better estimate.

A Titanic disaster In 1912the luxury liner Titanic, on its first voyage across the Atlantic, struck an iceberg and sank. Some passengers got off the ship in lifeboats, but many died. The two-way table gives information about adult passengers who lived and who died, by class of travel. Suppose we choose an adult passenger at random.

(a) Given that the person selected was in first class, what鈥檚 the probability that he or she survived?

(b) If the person selected survived, what鈥檚 the probability that he or she was a third-class passenger?

Is this valid? Determine whether each of the following simulation designs is valid. Justify your answer.

(a) According to a recent poll, 75% of American adults regularly recycle. To simulate choosing a random sample of 100 U.S. adults and seeing how many

of them recycle, roll a 4-sided die 100 times. A result of 1,2, or 3 means the person recycles; a 4 means that the person doesn鈥檛 recycle.

(b) An archer hits the center of the target with 60% of her shots. To simulate having her shoot 10 times, use a coin. Flip the coin once for each of the 10

shots. If it lands heads, then she hits the center of the target. If the coin lands tails, she doesn鈥檛.
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