Suppose a basketball player has made 265 out of 312 free throws. If the player makes the next 2 free throws, I will pay you $15. Otherwise you pay me $36.

Loss of $1.67

Step-by-step explanation:

The percentage of throwing 256 throws out of 312 is 256/312

= 0.8205 = 82.05%

Probability of making the next 2 shots is (0.8205) ^2 = 0.6732

Pr (of making both shots) = 0.6732

Pr (of missing both) = 1 - 0.6732

= 0.3268

Value when you win = $15

Value when you lose = - $36

Expected value = Pr (makes both) * value when you win + Pr (misses both) * value when you lose

= (0.6732 * 15) + (0.3268*-36)

= 10.098 + (-11.7684)

= 10.098 - 11.7684

= - 1.67

The player is expected to lose $1.67. It is not worth it.