Question

An integer is chosen between 0 and 100. What is the probability that it is
(i) divisible by 7 (ii) not divisible by 7?

Answer 1

The number of integers between 0 and 100 is n(S)=99
(i) Let `E_(1)`=Event of chosing on integer which is divisible by 7
=Event of choosing an integer which si multiple of 7
=(7,14,21,28,35,42,49,56,67,70,77,84,91,98)
`n(E_(1))=14`
`P(E_(1))=(n(E_(1)))/(n(S))=(14)/(99)`
(ii) Let `E_(2)` =Event of choosing an integer which is not divisible by 7
`n(E_(2))=n(S)-n(E_(1))`
=99-14=85
`P(E_(2))=(n(E_(2)))/(n(S))=(85)/(99)`