6-29. Suppose an individual stands at the free throw line on a basketball court and shoots until she makes a basket. Let the free throws be independent. If experience dictates that this person has an 80% chance of making each free throw, find the probability that it takes five shots to make the first basket.

What is the probability that it takes fewer than five throws? What is the probability that it takes at least six shots? What is the average number of shots made?