Amaya and Bo each roll a fair, ordinary six-sided die with the numbers 1,2,3,4,5,6 on the sides. What is the probability that Amaya rolls a greater number than Bo?
Enter your answer as a fraction in simplified form.
due to the symmetry of the problem the probability that Bo rolls greater than Amaya equals the probability that Amaya rolls greater than Bo.
The probability that they roll the same is 6/36=1/6
So the probability that they do not roll the same is 1-1/6 = 5/6
And thus the probability Amaya rolls greater than Bo is half of this or (5/6)/2 = 5/12