Question

Suppose a basketball player has made 265265 out of 312312 free throws. If the player makes the next 22 free throws, I will pay you $15$⁢15. Otherwise you pay me $36$⁢36.

Step 2 of 2 :  

If you played this game 756756 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be entered as negative.

Answer 1

Answer

probability of making a free throw = (favorale outcome)/(total outcome)

= 265/312

Probability of making next 2 free throws = P(A)*P(B)

where P(A) = P(B) = 265/312

so, we get P(next 2 free throws) = 265/312 * 265/312 = 0.7214

Probability of not making next 2 free throws= 1 - 0.7214 = 0.2786

E[x] = P(win)*$15 -P(loss)*$36

= 0.7214*15 - 0.2786*36

= 10.821 - 10.030

= $0.7914 (net profit)

If we play 756 games

then, we get

=n*E[x]

= 756*0.7914

=$ 598.71 (rounded to 2 decimals)