Question

A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?

Answer 1

i would say about $10 about 1/6th the time

Answer 2

$30

Explanation:

To find the expected value, first we find the outcomes for the sample space.

Rolling a 6-sided die, we have

1, 2, 3, 4, 5, 6

There are 2 values that are whole number multiples of 3: 3 and 6.

There is a 1/6 chance of rolling a 3 and a 1/6 chance of rolling a 6.

There is a 1/6 chance of rolling a 1, 1/6 chance of rolling a 2, 1/6 chance of rolling a 4, and 1/6 chance of rolling a 5.

Next we multiply the value won or lost by each probability.

If the player rolls a 3, they win 3(20) = 60. Multiplying it by its probability, we have

1/6(60) = 60/6 = 10

If the player rolls a 6, they win 6(20) = 120. Multiplying it by its probability, we have

1/6(120) = 120/6 = 20.

If the player rolls a 1, 2, 4 or 5, they win nothing. 0 times all of these will be 0.

Lastly, we add together these products:

10+20+0+0+0+0 = 30