Question

Consider the following game: Roll a fair 6-sided die. You win if the result is greater than 4; otherwise, you lose. To play, you must pay $4. If you win, you get $8; if you lose, the $4 fee is forfeited. What is the expected value for the amount gained/lost

Answer 1

Answer:

-$1.33 or lose $1.33

Step-by-step explanation:

In this game, there are two possible outcomes.

- There is a 2 in 6 chance (rolling a 5 or a 6) that you win $8.

- There is a 4 in 6 chance (rolling a 1, 2, 3 or a 4) that you win nothing.

Note that for any outcome, you start off paying $4 to play.

The expected value of this game is:

$E(X) =\frac{2}{6} *\ 8+\frac{4}{6}*\ 0-\ 4\\E(X) = -\ 1.33$

You are expected to lose $1.33 per play.