2005 Alabama ARML TST Problems/Problem 1
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.
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 .
|2005 Alabama ARML TST (Problems)|
|1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15|