Two independent rolls of a fair die are made. What is the probability that both rolls show an even number?

• A. 1/2
• B. 1/8
• C. 1/4
• D. 1

Answer: (C)

When events don't affect each other, the probability of both happening is found by multiplying their individual probabilities. For one roll of a fair die, there are three even outcomes (2, 4, 6) out of six, so the chance of an even result is 3/6 = 1/2. Since the two rolls are independent, the probability that both are even is (1/2) × (1/2) = 1/4. So the probability that both rolls show an even number is 1/4. This isn’t 1/2 (that would be just one roll), not 1/8 (that would come from multiplying three halves by mistake), and not 1 (which would mean it always happens).