Question

Two dice are rolled once. Find the probability of getting such numbers on the two dice, whose product is 12.

Answer 1

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`