Question

Suppose an NBA basketball player shooting an un- contested 2-point shot will make the basket with probability 0.6. However, if you foul the shooter, the shot will be missed, but two free throws will be awarded. Each free throw is an independent Bernoulli trial with success probability p. Based on the expected number of points the shooter will score, for what values of p may it be desirable to foul the shooter?

Answer 1

For values of p < 0.6, it may be desirable to foul the shooter.

Explanation:

Suppose an NBA basketball player shooting an un- contested 2-point shot will make the basket with probability 0.6.

This means that the amount of points he expects to score with the ball in his hand is:

2*0.6 = 1.2

Based on the expected number of points the shooter will score, for what values of p may it be desirable to foul the shooter?

The expected number of points he will score with these free throws is:

2p

In which p is the probability of making the free throw.

If will be desirable to foul the shooter is:

`2p < 1.2`

`p < (1.2)/(2)`

`p < 0.6`

For values of p < 0.6, it may be desirable to foul the shooter.