In a game of chance, two pyramid-shaped, four-sided dice (with sides 1, 2, 3, 4). one colored red and the other colored green, a
re rolled and their individual totals are added. If the sum of the 2 four-sided dice exceeds 5 (result from red die + result from green die > 5), the roller wins. If the sum is 5 or less, the roller loses. What is the probability of winning on a single play?
There are 4 possible outcomes for each die, which gives us 16 possible combinations (4 x 4). In order for the sum to exceed 5, the possible outcomes are:
Red = 3, and Green = 3
Red = 3, and Green = 4
Red = 4, and Green = 3
Red = 4, and Green = 4
Therefore, the probability of winning on a single play is: