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Question
Two dice are rolled once. Find the probability of getting such numbers on the two dice, whose product is 12.
Solution
The sample space of the given experiment is as follows:
`s={[(1,1) (1,2)(1,3)(1,4)(1,5)(1,6)],[(2,1) (2,2)(2,3)(2,4)(2,5)(2,6)],[(3,1) (2,2)(3,3)(3,4)(3,5)(3,6)],[(4,1) (4,2)(4,3)(4,4)(4,5)(14,6)],[(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)],[(6,1) (6,2)(6,3)(6,4)(6,5)(6,6)]}`
∴ n (S) = 36
Let E be the event of getting such numbers whose product is 12.
Then, E = {(2, 6), (3, 4), (4, 3), (6, 2)}
∴ n (E) = 4
Thus, required probability `(n(E))/(n(S))=4/36=1/9`
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