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प्रश्न
If two dice are rolled simultaneously, find the probability of the following event.
The digit on the first die is greater than the digit on second die.
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 C: digit on the first die is greater than the digit on second die
C = {(2,1), (3,1), (3,2), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (5,4), (6,1), (6,2), (6,3), (6,4), (6,5)}
∴ n(C) = 15
`therefore P (C) =(n(C))/(n(S))`
`=15/36`
`=5/12`
Hence, the probability that digit on the first die is greater than the digit on second die is `=5/12`
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(2) The sum of the numbers on their upper faces is divisible by 5.
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