Question

Suppose a basketball player has made 282 out of 393 free throws. If the player makes the next 2 free throws, I will pay you $6. Otherwise you pay me $8.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.

Answer 1

Answer:

-$ 0.79

Step-by-step explanation:

Since, the player has made 282 out of 393 free throws,

So, the probability of a free throw = $\frac{282}{393}$,

Thus, the probability of 2 free throws = $\frac{282}{393}\times \frac{282}{393}=\frac{8836}{17161}$

And, the probability of not getting 2 free throws = $1-\frac{8836}{17161}=\frac{8325}{17161}$

Given, the price of winning ( getting 2 free throws ) is $6 while the price of losing ( not getting 2 free throws ) is - $ 8 ( ∵ there is a loss of $ 8 ),

Hence, the expected value of the proposition = probability of winning × winning value + probability of losing × losing value

$= \frac{8836}{17161}\times 6 + \frac{8325}{17161}\times -8$

$=\frac{53016}{17161}-\frac{66600}{17161}$

$=-\frac{13584}{17161}$

$=-\ 0.79156226327$

$\approx -\ 0.79$