Problem:
The faces of a cubical die are marked with the numbers , and . The faces of a second cubical die are marked with the numbers , and . Both dice are thrown. What is the probability that the sum of the two top numbers will be , or ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Of the possible outcomes, the four pairs , and yield a sum of . The six pairs , and yield a sum of . The four pairs , and yield a sum of . Thus the probability of getting a sum of , or is .
Note: The dice described here are known as Sicherman dice. The probability of obtaining each sum between and is the same as that on a pair of standard dice.
The problems on this page are the property of the MAA's American Mathematics Competitions