Chapter 6, Problem 66SE

Identifying $n,p$, and $x$ For each situation, identify the sample size $n$, the probability of a success $p$, and the number of success $x$. When asked for the probability, state the answer in the form $b\left(n,p,x\right)$. There is no need to give the numerical value of the probability. Assume the conditions for a binomial experiment are satisfied.

Since the Surgeon General’s Report on Smoking and Health in 1964 linked smoking to adverse health effects, the rate of smoking the United States have been falling. According to the Centers for Disease Control and Prevention in 2016, 15% of U.S. adults smoked cigarettes (down from 42% in the 1960s).

a. If 30 Americans are randomly selected, what is the probability that exactly 10 are smokers?

b. If 30 Americans are randomly selected, what is the probability that exactly 25 are not smokers?