### Instruction: Geoff and Trevor each roll a fair six-sided die.  What is the probability that the product of the numbers they roll is even?### Response: I need to find the fraction of outcomes where the product is even, out of all the possible outcomes.
There are 6 x 6 = 36 possible outcomes, since each die can roll any of the six numbers.
The product is even if and only if at least one of the dice shows an even number.
There are 3 even numbers and 3 odd numbers on each die, so the probability that one die shows an even number is 3/6 = 1/2.
If I use the complement rule, I can find the probability that both dice show odd numbers, and then subtract that from 1 to get the probability that at least one die shows an even number.
The probability that both dice show odd numbers is (3/6) x (3/6) = 9/36.
So the probability that at least one die shows an even number is 1 - 9/36 = 27/36.