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

Answer:

-$0.90

Step-by-step 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:

$P(W) = \frac{217}{302}*\frac{217}{302}*\frac{217}{302}\\P(W) = 0.37098$

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