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Suppose a basketball player has made 217217 out of 357357 free throws. If the player makes the next 22 free throws, I will pay you $32$⁢32. Otherwise you pay me $21$⁢21. 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: The expected value would be -$9.022.

Step-by-step explanation:

Since we have given that

Number of throws made by basketball player = 217

Number of free throws = 357

So, [tex]p=\dfrac{217}{357}=0.61[/tex]

Let X be the amount he lose or win.

X can be $32 or -$21

So, it becomes,

[tex]P(X=32)=0.61\times 0.61\times 0.61=0.226[/tex]

and

[tex]P(X=-21)=1-0.226=0.774[/tex]

So, the expected value would be

[tex]E[x]=P(X=32)\times 32+P(X=-21)\times -21\\\\=0.226\times 32+0.774\times -21\\\\=-9.022[/tex]

Hence, the expected value would be -$9.022.

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