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.

Question

Orion Solis

Mathematics

9 March, 22:22

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.

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Bruce Burke · 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.