19. The National Basketball Association (NBA) records a variety of statistics for each team.

Two of these statistics are the percentage of field goals made by the team and the percentage of three-point shots made by the team. For a portion of the 2004 season, the shooting records of the 29 teams in the NBA showed the probability of scoring two points by making a field goal was .44, and the probability of scoring three points by making a three-point shot was .34 (http://www.nba.com, January 3, 2004).

a. What is the expected value of a two-point shot for these teams?

b. What is the expected value of a three-point shot for these teams?

c. If the probability of making a two-point shot is greater than the probability of making a three-point shot, why do coaches allow some players to shoot the three-point shot if they have the opportunity? Use expected value to explain your answer.