GATE 2023 BT – Question 33
Two fair six-sided dice are thrown. The probability of getting 12 as the product of the numbers on the dice (rounded off to two decimal places) is ____________.
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Correct answer: 0.10 to 0.12
Explanation
There are $6\times6=36$ equally likely ordered outcomes.
**Product = 12.** The factor pairs of 12 with both factors from 1 to 6 are $(2,6)$ and $(3,4)$. Each can occur in two orders:
$$(2,6),\ (6,2),\ (3,4),\ (4,3)\;\Rightarrow\;4\text{ outcomes}.$$
(1 × 12 and 12 × 1 are not possible because a die shows at most 6.)
$$P=\frac4{36}=\frac19=0.111\approx\mathbf{0.11}.$$