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Question
Two dice are rolled once. Find the probability of getting such numbers on two dice whose product is a perfect square.
Solution
Number of possible outcomes = 36
Let E be the event of getting two numbers whose product is a perfect square.
Then, the favourable outcomes are (1, 1), (1, 4), (4, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6).
Number of favourable outcomes = 8.
∴ P(getting numbers whose product is a perfect square) = `("Number of favourable outcomes")/"Number of all possible outcomes"`
`= 8/36 = 2/9`
Thus, the probability of getting such numbers on two dice whose product is a perfect square is `2/9`.
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