expected value of proposition and expected wins and losses

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

The player shooting 390/434 is a free throw percentage of 89.86%.  We can now estimate his probability of making the next 2 shots as (.8986)^2 = .8075.

 

So now to find the expected value, you just need to find the value of each possible outcomes (he makes both or he doesn't).

 

P(makes both) * (Value when you win) + P(misses both) * (value when you lose)

.8075 * $40 + (1-.8075)*(-$169)

32.2 - 32.53

= -$.23

 

For the second part, you already know the expected value of each possible game. So now you just need to multiply that by 588 to get your expected loss on 588 games.