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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.

Respuesta :

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 = [tex]\frac{282}{393}[/tex],

Thus, the probability of 2 free throws = [tex]\frac{282}{393}\times \frac{282}{393}=\frac{8836}{17161}[/tex]

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

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

[tex]= \frac{8836}{17161}\times 6 + \frac{8325}{17161}\times -8[/tex]

[tex]=\frac{53016}{17161}-\frac{66600}{17161}[/tex]

[tex]=-\frac{13584}{17161}[/tex]

[tex]=-\$ 0.79156226327[/tex]

[tex]\approx -\$ 0.79[/tex]

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