A fair six-sided die is rolled twice. What is the probability that the product of the two numbers rolled is even?

Correct answer

C. 3/4

Principle or equation

For independent events, P(A and B) = P(A)P(B). The product of two integers is odd only if both are odd. Use complementary probability.

Why this answer is correct

Total outcomes = 6 * 6 = 36. Product is odd only when both rolls are odd. Probability of odd on one roll = 3/6 = 1/2. So P(both odd) = (1/2)*(1/2) = 1/4. Thus P(product even) = 1 - 1/4 = 3/4.

Example

Rolling a 3 and a 5 gives product 15 (odd). Rolling a 2 and a 3 gives product 6 (even).