Two dice are thrown simultaneously. What is the probability that the product of the two numbers is even?

Given data

• Each die shows 1–6 with equal probability.

Concept/ApproachThe product is even unless both outcomes are odd. Compute P(both odd) and subtract from 1.

Step-by-step calculationP(odd on one die) = 3/6 = 1/2P(both odd) = (1/2) × (1/2) = 1/4P(product even) = 1 − 1/4 = 3/4

Verification/AlternativeComplementary counting among 36 outcomes: 9 odd-odd pairs (3×3) ⇒ 36 − 9 = 27 even-product outcomes ⇒ 27/36 = 3/4.

Common pitfallsCounting only pairs with at least one even face but forgetting total outcomes are ordered.

Final Answer3/4