Question

A game is played as follows: a die numbered 1 to 6 is rolled. If the number 1 comes up, you get nothing. If the number 2, 3, or 5 comes up, you win $4. If the number 4 or 6 comes up, you lose $6. According to the expected value, this is a fair game.

Answer 1

1/6 chance of nothing

3/6 or 1/2 chance of $4

2/6 or 1/3 chance of -$6

Answer 2

Fair game.

Explanation:

Prob(getting a 1) = 1/6

Prob(getting a 2,3 or 5) = 3/6 = 1/2

Prob(getting a 4 or a 6) = 2/6 = 1/3.

The expected value = 0*1/6 + 1/2*4 + 1/3*(-6)

= 0 + 2 - 2

= 0.

The net value is zero so it is a fair game.