An integer is chosen between 0 and 100. What is the probability that it is

(i) divisible by 7?

(ii) not divisible by 7?

On choosing an integer between 0 and 100,

Sample space = {1, 2, 3, 4, …….., 99}.

(i) Let E₁ be the event of choosing a number that is divisible by 7.

E₁ = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98}.

∴ The number of favourable outcomes to the event E₁ = 14.

$\therefore P(E$1) = \dfrac{\text{No. of favourable outcomes to } E1}{\text{Total no. of possible outcomes}} = \dfrac{14}{99}.

Hence, the probability of choosing an integer divisible by 7 is $\dfrac{14}{99}$.

(ii) Let E₂ be the event of choosing a number that is not divisible by 7.

Since there are 14 numbers between 0 and 100 that are divisible by 7, hence the numbers not divisible by 7 = 99 - 14 = 85.

$\therefore P(E$2) = \dfrac{\text{No. of favourable outcomes to } E2}{\text{Total no. of possible outcomes}} = \dfrac{85}{99}.

Hence, the probability of choosing an integer not divisible by 7 is $\dfrac{85}{99}.$