5.73 Driver’s exam Three 15-year-old friends with no particular background in driver’s education decide to take the written part of the Georgia Driver’s Exam. Each exam was graded as a pass (P) or a failure (F).

a. How many outcomes are possible for the grades received by the three friends together? Using a tree diagram, list the sample space.

b. If the outcomes in the sample space in part a are equally likely, find the probability that all three pass the exam.

c. In practice, the outcomes in part a are not equally likely.
Suppose that statewide 70% of 15-year-olds pass the exam. If these three friends were a random sample of their age group, find the probability that all three pass.

d. In practice, explain why probabilities that apply to a random sample are not likely to be valid for a sample of three friends.