Answer:
For values of p < 0.6, it may be desirable to foul the shooter.
Step-by-step 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:
[tex]2p < 1.2[/tex]
[tex]p < \frac{1.2}{2}[/tex]
[tex]p < 0.6[/tex]
For values of p < 0.6, it may be desirable to foul the shooter.
