Question

Suppose a basketball player has made 191 out of 325 free throws. If the player makes the next 2 free throws, I will pay you $11. Otherwise you pay me $7. 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

The expected value of the proposition is $3.58.

Step-by-step explanation:

The expected value of a proposition is calculated by multiplying each possible outcome by its probability and then summing them up. In this case, the basketball player has made 191 out of 325 free throws. The probability of making a free throw is 191/325 and the probability of missing a free throw is 1 - (191/325). The expected value can be calculated as follows:

Expected value = (Pr(Make)*Winnings(Make)) + (Pr(Miss)*Winnings(Miss))

= ((191/325)*11) + ((1 - (191/325))*(-7))

= 6.806 + (-3.226)

= 3.58

Therefore, the expected value of the proposition is $3.58.