Chapter 5.3, Problem 34PB

Go Celtics! Larry Bird, who played pro basketball for the Boston Celtics, was known for being a good shooter. In games during 1980–1982, when he missed his first free throw, 48 out of 53 times he made the second one, and when he made his first free throw, 251 out of 285 times he made the second one.

1. a. Form a contingency table that cross tabulates the outcome of the first free throw (made or missed) in the rows and the outcome of the second free throw (made or missed) in the columns.
2. b. For a given pair of free throws, estimate the probability that Bird (i) made the first free throw and (ii) made the second free throw. (Hint: Use counts in the (i) row margin and (ii) column margin.)
3. c. Estimate the probability that Bird made the second free throw, given that he made the first one. Does it seem as if his success on the second shot depends strongly, or hardly at all, on whether he made the first?