Question

A game is played using one die. if the die is rolled and shows a 2, the player wins $45. If the die shows any number other than 2, the player wins nothing.

If there is a charge of $9 to play the game what is the games expected value?

Answer 1

The game's expected value is of -$1.5.

Explanation:

Expected value:

Probability of each outcome multiplied by the outcome.

One out of 6 sides is 2:

1/6 probability of the player earning 45 - 9 = $36.

5/6 probability of the player losing $9. So

`E = 36(1)/(6) - 9(5)/(6) = (36 - 45)/(6) = -(9)/(6) = -1.5`

The game's expected value is of -$1.5.