Question

Consider a game in which a player rolls one die. If an even number comes​ up, the player wins the number of dollars showing on the die. If an odd number comes​ up, the player loses the number of dollars showing on the die. Calculate the expected value for this game. Is the game​ fair? (Assume that there is no cost to play the​ game.)

Answer 1

Yes

Explanation:

Winning numbers: 2, 4, 6

Losing numbers: 1, 3, 5

The even numbers are greater.

The average even (winning) number is 4.

The average odd (losing) number is 3.

You can win half a dollar on average.

Equation: (1/6)(-1)+(1/6)(2)+(1/6)(-3)+(1/6)(4)+(1/6)(-5)+1/6(6) = 0.5