Q:

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.

Accepted Solution

A:
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.