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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 at least 10.
Solution
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 A: sum of the digits on the upper faces is at least 10
A = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)}
∴ n(A) = 6
∴ `P(A) = (n(A))/(n(S))`
= `6/36`
= `1/6`
Hence, the probability that the sum of the digits on the upper faces is at least 10 is `1/6`.
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