Question

Suppose a basketball player has made 217 out of 302 free throws. If the player makes the next 3 free throws, I will pay you $23. Otherwise you pay me $15. 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

-$0.90

Explanation:

There are only two possible outcomes, winning $23 (W) or losing $15 (L). Therefore:

`P(W) + P(L) = 1`

The probability of the player making his next 3 free throws (P(W)) is:

`P(W) = (217)/(302)*(217)/(302)*(217)/(302)\\P(W) = 0.37098`

The probability of the player NOT making his next 3 free throws (P(L)) is:

`P(L) = 1 - P(W) = 1 - 0.37098\\P(L) = 0.62902`

Expected value (EV) is given by the payoff of each outcome multiplied by its probability:

`EV = (23*0.37098) -(15*0.62902)\\EV = -\$0.90`

The expected value of the proposition is -$0.90