Question

Suppose a basketball player has made 233 out of 402 free throws. if the player makes the next 3 free throws, i will pay you $166. otherwise you pay me $40. 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 is $0.11.

The probability that the player will make the next free throw is 233/402. The probability that the next 3 are made will be (233/402)^3. To find the expected value of this, we multiply by the winnings we would have in this case, 166. So far we have:

((233/402)^3)(166)

The probability that the next 3 are not made is 1-((233/402)^3). Multiply this by the loss, -40, to get its expected value. This gets us to:

((233/402)^3)(166)-(1-((233/402)^3)).

This comes out to $0.11.

Answer 2

There expected value of the proposition for you is -11 cents, that is, you are expected to lose $0.11.

Explanation:

The first step to solve this problem is finding the probability that he makes 3 of his next 3 free throws.

The problem states that he makes 233 out of 402 free throws. This means that the probability that he makes a free throw is
`p = (233)/(402) = 0.5796`.

The probability that he makes his next 3 free throws is
`P = 0.5796^(3) = 0.1947`

if the player makes the next 3 free throws, i will pay you $166. otherwise you pay me $40.

There is a 19.47% probability of him making the next three free throws. This means that there is a 19.47% probbability of you losing $166.

There is a 100-19.47 = 80.53% probability of him not making the next three free throws. This means that there is an 80.53% probability of you winning $40.

So, for you, the expected value of the proposition is:

`E = 0.8053*(40) -166*(0.1947) = -0.11`

There expected value of the proposition for you is -11 cents.