Question 6.166

68. Geometric Probability Distribution. Refer to Example 14(a), where a fisherman is going fishing and will continue to fish until he catches a rainbow trout. This is an example of the geometric probability distribution, which has the same requirements as the binomial distribution, except that there is not a fixed number of trials . Instead, the geometric random variable represents the number of trials until a success is observed. The geometric probability distribution formula is

where represents the probability of success. The possible values of are . The U.S. Census Bureau reported in 2010 that 30% of U.S. households have no access at all to the Internet. A random sample is taken of U.S. households. Let the random variable represent the number of trials until a household is found that has access to the Internet.

  1. Find the probability that , that is, the first household sampled has access to the Internet.
  2. Find the probability that , that is, the first household sampled does not have access, but the second household sampled does have access to the Internet.
  3. Find the probability that , that is, the first two households sampled do not have access, but the third household sampled does have access to the Internet.