2005 Alabama ARML TST Problems/Problem 1
Problem
Two six-sided dice are constructed such that each face is equally likely to show up when rolled. The numbers on the faces of one of the dice are . The numbers on the faces of the other die are . Find the probability of rolling a sum of with these two dice.
Solution
We use generating functions to represent the sum of the two dice rolls:
The coefficient of , that is, the number of ways of rolling a sum of 9, is thus , out of a total of possible two-roll combinations, for a probability of .
Alternatively, just note the possible pairs which work: and are all possible combinations that give us a sum of (where we count twice because there are two different s to roll). Thus the probability of one of these outcomes is .
See also
2005 Alabama ARML TST (Problems) | ||
Preceded by: First question |
Followed by: Problem 2 | |
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