Solve the following:
Q1. In a recent poll of married couples, about 79 percent of the men and 55 percent of the women were employed outside the home. In 39 percent of the couples, both the husband and the wife work outside the home.
Find the probability that in a randomly selected couple either the husband or his wife works outside the home.
Q2. A despondent math professor is traveling to Las Vegas to bet his entire life savings, $20,000 on one roll of the (two) dice. If the total is 7 or 11, he will take home $100,000; otherwise, he forfeits his savings.
What is his mathematical expectation?
Q3. According to the Bureau of Navel (sic) Standards, 75 percent of all people are "inners," (that is, their belly buttons poke inward) ; everyone else is an "outer." Let the random variable x be the number of outers among 7 randomly selected persons.
A. Find the mean and variance of x.
B. Find the probability that exactly 2 of the 7 persons are outers.
C. Find the probability that no more than 6 of the 7 are outers.
D. Find the probability that none of the 7 is an outer.