GATE 2021 AE – Question 3
Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:
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Correct answer: (D) 1/4
Explanation
The two dice are independent. On one die, 3 of the 6 faces (2, 4, 6) are even, so
$$P(\text{even on one die})=\frac36=\frac12 .$$
For both dice to show an even number:
$$P=\frac12\times\frac12=\frac14 .$$
(Check by counting: $3\times3=9$ favourable outcomes out of $36$, and $9/36=1/4$.)
Answer **1/4** (D).