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 E_{1} = 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(E_{1}) = 14

(ii) Let Event of choosing an integer which is not divisible by 7

∴ n(E_{2}) = n(S) - n(E_{1})

= 99 - 14 = 85

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