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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.
Solution
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.
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