Question

Suppose a basketball player has made 390 out of 434 free throws. If the player makes the next 2 free throws, I will pay you $40.Otherwise you pay me $169

Step 1 of 2: Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Step 2 of 2: If you played this game 588 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: a) -$0.19, b) -$111.72 .

Step-by-step explanation:

Since we have given that

Number of free throws = 434

Number of throws made by them = 390

Amount for making the next 2 free throws = $40

Amount otherwise he has to pay = $169

a) Find the expected value of the proposition.

Expected value of success in next 2 free throws = $\dfrac{390}{434}\times \dfrac{391}{435}=0.8077$

Expected value would be

$0.8077\times 40+(1-0.8077)\times -169\\\\=32.308-32.4987\\\\=-\ 0.19$

b)  If you played this game 588 times how much would you expect to win or lose?

Number of times they played the game = 588

So, Expected value would be

$588\times -0.19\\\\=-\ 111.72$

Hence, a) -$0.19, b) -$111.72