Suppose that $20,000$ married adults in the United States were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have.

a. Find the probability that a married adult has three children.

b. In words, what does the expected value in this example represent?

c. Find the expected value.

d. Is it more likely that a married adult will have two to three children or four to six children? How do you know?

Given the results of a survey conducted on the number of children married adults have.

Because the sum of all probabilities for a random variable is 1, the probability x=3 equals 1-sum of all probabilities.

Given the results of a survey conducted on the number of children married adults have.

The expected value in the scenario in question represents the average number of children a married couple has.

Given the results of a survey conducted on the number of children married adults have.

$$\begin{gathered} E\left(x\right)=\underset{}{\sum \left[x.P\left(x\right)\right]} \\ E\left(x\right)=2.35 \end{gathered}$$

Given the results of a survey conducted on the number of children married adults have.

A married adult with two to three children is more likely to have two to three children than a married adult with four to six children because the likelihood of having two to three children is greater than the probability of having four to six children. A person's chances of having two to three children are 0.50, while his or her chances of having four to six children are 0.20.