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Suppose a basketball player has made 291 out of 389 free throws. If the player makes the next 2 free throws, I will pay you $38. Otherwise you pay me $50. 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 of the proposition is -$0.76.

Step-by-step explanation:

It is provided that a basketball player has made 291 out of 389 free throws.

Then rate of him making a free throw is,

[tex]P(\text{free throw})=\frac{291}{389}=0.7481[/tex]

The probability that he makes the next 2 free throws is:

[tex]P(\text{Next 2 free throws})=(0.7481)^{2}=0.5596[/tex]

The payout rules are:

  • If the player makes the next 2 free throws, I will pay you $38.
  • Otherwise you pay me $50.

Compute the expected value of the proposition as follows:

Expected value = $38 × P (Makes both) + (-$50) × P (Misses both)

                          [tex]=($38\times 0.5596)+(-$50\times (1-0.5596))\\=21.2648-22.02\\=-0.7552\\\approx -$0.76[/tex]

Thus, the expected value of the proposition is -$0.76.

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