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प्रश्न
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.
उत्तर
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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