An integer is chosen between 0 and 1000. What is the probability that it is
(i) divisible by 7?
(ii) not divisible by 7?
The number of integers between 0 and 100 is n(S) = 99
(i) Let E1 = Event of choosing an integer which is divisible by 7
= Event of choosing and integer which is multiple of 7
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98}
∴ n(E1) = 14
(ii) Let Event of choosing an integer which is not divisible by 7
∴ n(E2) = n(S) - n(E1)
= 99 - 14 = 85
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