# An integer is chosen at random between 1 and 100

Probability (C10)
An integer is chosen at random between 1 and 100. Find the probability that it is:

- divisible by 8
- not divisible by 8

### Answer

Number of integers between 1 and 100: 2, 3 , 4, 5 , ..., 99

Total number of outcomes = 98

(i) Numbers which are divisible by 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

Favourable Outcomes = 12

Probability that integer is divisible by 8, P(E) = 12/98 or 6/49

(ii) Probability that integer is not divisible by 8

P(E') = 1 - probability that it is divisible by 8

= 1 - 6/49

= 43/49