A fair six-sided die is rolled twice. What is the probability that the product of the two numbers is even?
Show the answer and explanation
Correct answer
C. 3/4
Principle or equation
The product of two integers is even if at least one of them is even. For independent events, P(at least one even) = 1 - P(both odd).
Why this answer is correct
Each die has 3 odd numbers (1,3,5) and 3 even numbers (2,4,6). P(both odd) = (3/6)*(3/6) = 1/4. Therefore, P(product even) = 1 - 1/4 = 3/4.
Example
If rolling a die twice, the probability of getting at least one 6 is 1 - (5/6)^2 = 11/36.
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