According to a January 2013 survey by the Pew Research Center, the percentage of Americans who trust the government in Washington has decreased steadily since Bill Clinton left office.6 Today, approximately 30% of Americans say they trust the government (always or most of the time). Suppose three Americans are selected at random. Let X be the number who trust the government.
a. Construct the probability distribution for X. Construct the corresponding probability histogram.
b. What is the probability that all three Americans trust the government?
c. What is the probability that at least one of the three trusts the government?
Twinkies are an American tradition, sold for over 83 years, originating in a Chicago bakery, and forever linked to legal lingo. (You may have read about the “Twinkie defense,” associated with a 1979 murder trial in San Francisco.) Approximately 12% of households in the United States buy Twinkies.7 Suppose four households are selected at random and let Y be the total number of households that buy Twinkies.
a. Construct the probability distribution for Y. Write a Solution Trail for this problem.
b. What is the probability that at least one household buys Twinkies?
c. Suppose at least two households buy Twinkies. What is the probability that all four households buy Twinkies?
Staples has six special drafting pencils for sale, two of which are defective. A student buys two of these six drafting pencils, selected at random. Let the random variable X be the number of defective pencils purchased. Construct the probability distribution for X.
Two packages are independently shipped from Fort Collins, Colorado, to the Convention Center in Kansas City, Missouri, and each is guaranteed to arrive within four days. The probability that a package arrives within one day is 0.10, within two days is 0.15, within three days is 0.25, and on the fourth day is 0.50. Let the random variable X be the total number of days for both packages to arrive. Construct the probability distribution for X.