In Exercises 29–32, use the given sample space or construct the required sample space to find the indicated probability.




Three Children Use this sample space listing the eight simple events that are possible when a couple has three children (as in Example 2): {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly one girl.

In Exercises 21-28, find the probability and answer the questions.

Social Networking In a Pew Research Center survey of Internet users, 3732 respondents say that they use social networking sites and 1380 respondents say that they do not use social networking sites. What is the probability that a randomly selected person uses a social networking site? Does that result suggest that it is likely (with a probability of 0.5 or greater) for someone to use social networking sites?

In Exercises 21-28, find the probability and answer the questions.

Genetics: Eye Color Each of two parents has the genotype brown/blue, which consists of the pair of alleles that determine eye color, and each parent contributes one of those alleles to a child. Assume that if the child has at least one brown allele, that color will dominate and the eyes will be brown. (The actual determination of eye color is more complicated than that.)

b. What is the probability that a child of these parents will have the blue/blue genotype?

In Exercises 21-28, find the probability and answer the questions.

X-Linked Genetic Disease Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. In the following, represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child.

a. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a son will inherit the disease?

In Exercises 21-28, find the probability and answer the questions.

X-Linked Genetic Disease Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is not defective. In the following, represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child.

c. If a mother has one defective x chromosome and one good X chromosome and the father has good XY chromosomes, what is the probability that a son will inherit the disease?

In Exercises 29–32, use the given sample space or construct the required sample space to find the indicated probability.

Four Children Exercise 29 lists the sample space for a couple having three children. After identifying the sample space for a couple having four children, find the probability of getting three girls and one boy (in any order).

In Exercises 33–40, use the given probability value to determine whether the sample results are significant.

Voting Repeat the preceding Exercise 33 after replacing 40 Democrats being placed on the first line of voting ballots with 26 Democrats being placed on the first line. The probability of getting a result as high as 26 is 0.058638.

In Exercises 33–40, use the given probability value to determine whether the sample results are significant.

Voting Repeat Exercise 33 after replacing 40 Democrats being placed on the first line of voting ballots with 14 Democrats being placed on the first line. The probability of getting a result as low as 14 is 0.029792.

In Exercises 33–40, use the given probability value to determine whether the sample results are significant.

Voting Repeat Exercise 33 after replacing 40 Democrats being placed on the first line of voting ballots with 27 Democrats being placed on the first line. The probability of getting a result as high as 27 is 0.029792.