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

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?

 

a.$3.33

b.$6.66

c.$8.50

d.$30.00

e.$40.00

Answer 1

To find the expected value, you need to find the probability of each event, and multiply that by how much you would win when that event happens.

 

Roll a 1 - (1/6)(0) = 0 (no money, so no expected value)

Roll a 2 - (1/6)(0) = 0 (same deal)

Roll a 3 - (1/6)(60) = 10 (you would expect to get 10 dollars, 1/6th of the time)

 

Keep going like this, then add up the expected values for each number to find the overall expected value.