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

If the point guard takes the three, the expected value is: (3)(0.30) + (0)(0.70) = 0.9.
If he passes it to his teammate for a two-point shot, the expected value is (2)(0.48) + (0)(0.52) = 0.96.
Based on this, he should pass it to his teammate for a higher expected value.