Question

If two dice are rolled simultaneously, find the probability of the following event. The sum of the digits on the upper faces is 33.

Answer 1

If two dice are rolled simultaneously.

Sample Space (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)(3,2)(3,3)(3,4)(3,5)(3,6)],[(4,1) (4,2)(4,3)(4,4)(4,5)(4,6)],[(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

Event B: sum of the digits on the upper faces is 33
B = {}
∴ n(B) = 0 

`therefore P(B) = (n(B))/(n(S)`

`= 0/36`

  = 0

​Hence, the probability that the sum of the digits on the upper faces is 33 is 0.