Question

Roll a number cube. If the number cube comes up odd, you win the same number of points as the number on the cube. If the number comes up even, you lose 4 points. What is the expected number of points per roll?.

Answer 1

-0.5

Explanation:

Expected value is found by multiplying the probabilities of each roll by the amount won or lost with each roll.

The odd rolls are 1, 3 and 5. The probability of rolling a 1 is 1/6, and the value is 1; this gives us 1/6(1) = 1/6.

The probability of rolling a 3 is 1/6, and the value is 3; this gives us 1/6(3) = 3/6.

The probability of rolling a 5 is 1/6, and the value is 5; this gives us 1/6(5) = 5/6.

Rolling any even number gives us the same value. The probability of rolling an odd number is 3/6, and the value is -4; this gives us 3/6(-4) = -12/6.

Together we have

1/6+3/6+5/6-12/6 = 4/6+5/6-12/6 = 9/6-12/6 = -3/6 = -0.5