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

Solution-

The probability of making a single shot is,

$P(x)=\frac{204}{409}$

The probability of making 3 shot will be,

$P(x)=(\frac{204}{409})^3=0.1241$

The probability of not making 3 shot is,

$P'(x)=1-P(x)=1-(\frac{204}{409})^3=1-0.1241=0.8759$

The expected gain for the basketball player will be,

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

$=(0.1241)\times (17)+(0.8759)\times (-4)$

$=2.1097-3.5036$

$=-1.3939$

$=-1.39$

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

$=-1.39\times 921=-1280.19$

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