Question

Vlad is playing a dice game with Ulga.

Vlad will roll 2 six-sided dice, and if the sum of the dice is divisible by 3, he will win $6. If the sum is not divisible


by 3, he will lose $3.


What is Vlad's expected value of playing this game?


Round your answer to the nearest cent.

Answer 1

Vlad's expected value of playing this game is -$1.50

From the information, we have that;

There are 6 x 6 = 36 possible outcomes when rolling two dice.

Each outcome has equal probability (1/36).

Determine value for each outcome:

If the sum is divisible by 3 (e.g., 3, 6, 9, 12), Vlad wins $6.

If the sum is not divisible by 3 (all other outcomes), Vlad loses $3.

Expected value = (Probability of winning x Win amount) + (Probability of losing x Loss amount)

Probability of winning = Number of winning outcomes / Total outcomes = (6/36) = 1/6

Probability of losing = (30/36) = 5/6

= (1/6 * $6) + (5/6 * -$3)

= $1 +( -15/6)

= 1 - 0.25

= $ -1.50