Question

Suppose a basketball player has made

204 out of 409 free throws. If the player makes the next 3 free throws, I will pay you
$17. Otherwise you pay me $4.
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 921 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 probability of making a single shot is,

`P(x)=(204)/(409)`

The probability of making 3 shot will be,

`P(x)=((204)/(409))^3=0.1241`

The probability of not making 3 shot is,

`P'(x)=1-P(x)=1-((204)/(409))^3=1-0.1241=0.8759`

The expected gain for the basketball player will be,

= (Probability of making 3 shots) × ($17) + (Probability of NOT making 3 shots) x (-$4)

`=(0.1241)* (17)+(0.8759)* (-4)`

`=2.1097-3.5036`

`=-1.3939`

`=-1.39`

So the basketball player is expected to lose, on average, $1.39

If he played this game 921 times how much would you expect to win or lose

`=-1.39* 921=-1280.19`

So the basketball player is expected to lose $1280.19, if he plays this game 921 times.