Question

You have two six-sided dice. Die A has 2 twos, 1 three, 1 five, 1 ten, and 1 fourteen on its faces. Die B has a one, a three, a five, a seven, a nine, and an eleven on its faces. On any given roll of both dice, what is the probability that the number showing on Die A will be greater than the number on die B? What is the probability that the number showing on die B will be greater? Will fan and medal!

Answer 1

The 36 possible outcomes are as follows, with the number on die A on the left of each pair of numbers:

2,1 2,1 3,1 5,1 10,1 14,1
2,3 2,3 3,3 5,3 10,3 14,3
2,5 2,5 3,5 5,5 10,5 14,5
2,7 2,7 3,7 5,7 10,7 14,7
2,9 2,9 3,9 5,9 10,9 14,9
2,11 2,11 3,11 5,11 10,11 14,11
Now you need to find the number of outcomes where the number on die A is greater than the number of die B. Then divide that number of outcomes by 36, and simplify the resulting fraction to find the answer to the first part of the question.