Question

Instead of using the values {1, 2, 3, 4, 5, 6} on dice, suppose a pair of dice have the following {1, 2, 2, 3, 3, 4} on one die and {1, 3, 4, 5, 6, 8} on the other. Find the probability of rolling the sum of 7 with these dice. Be sure to reduce.

Answer 1

The dice will show a sum of 7 if you roll

• 1 and 6

• 2 and 5 (2 ways)

• 3 and 4 (3 ways)

so there are 6 ways of rolling a sum of 7. Out of 6 × 6 = 36 possible outcomes, the probability of rolling a sum of 7 is 6/36 = 1/6.