Question

Consider a game in which a player rolls one die. If an odd number comes​ up, the player wins the number of dollars showing on the die. If an even 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

The die has six sides.

Three are of an even (loosing) number: 2, 4, 6

Three of an an odd (winning) number: 1, 3, 5

The even numbers are greater.

The average even (loosing) number is 4.

The average odd (winning) number is 3.

On average, you can expect to loose half-a-dollar.

(If you want a math equation)

E=(1/6)(1)+(1/6)(-2)+(1/6)(3)+(1/6)(-4)+(1/6)(5)+1/6(-6)

E=(1/6) (1-2+3-4+5-6)=-3/6=-1/2