Question

a standard six-sided die is rolled twice. what is the probability that the product of the rolls is even?

Answer 1

• 3/4 or 0.75 or 75%

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The probability of rolling an even number on a single die is 3/6 or 1/2.

Consider the possible outcomes of rolling the two dice:

• If both dice are odd, the product will be odd;
• If both dice are even, the product will be even;
• If one die is even and one die is odd, the product will be even.

So, the only way to not have an even product is if both dice are odd.

The probability of rolling an odd number on a single die is also 1/2, so the probability of rolling two odd numbers is (1/2) x (1/2) = 1/4.

Therefore, the probability of rolling an even product is:

• 1 - 1/4 = 3/4 = 0.75 or 75%