Question

The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time.
Xi 3 0
P(xi) 0.30 0.70


Xi 2 0
P(xi) 0.48 0.52




What is the expected value for each choice?


Should he pass the ball or take the shot himself? Explain.

Answer 1

the expected value for the 3 point shot = (3 * 0.30) + (0 * 0.70) = 0.90

the expected value for the 2 point shot = (2 * 0.48) + (0 * 0.52) = 0.96

the expected value for the 2 point shot is higher than the 3 point shot so he should pass the ball