Two fair dice are tossed. One die is red and one die is green.

Calculate the probability that the sum of the numbers on the two dice is an odd number given that the number that shows on the red die is larger than the number that shows on the green die.

• 1/4
• 5/12
• 3/7
• 1/2
• 3/5

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

Of the 36 possible pairs, there are a total of 15 that have the red number larger than the green number. Note that a list is not needed. There are 6 that have equal numbers showing and of the remaining 30 one-half must have red larger than green. Of these 15, 9 have an odd sum for the answer, 9/15 = 3/5. This is best done by counting, with 3 combinations adding to 7, 2 combinations each totalling 5 and 9, and 1 combination each totalling 3 and 11.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.