Question

An integer is chosen at random between $1$ and $100$. Find the probability that it is not divisible by $8$.

Answer 1

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

Total number of outcomes $=98$

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 $8$-

$P\left(E\right)=\frac{12}{98}=\frac{6}{49}$

Probability that integer is not divisible by $8$-

$P\left(E^{\prime }\right)=1-P\left(E\right)$

$\Rightarrow P\left(E^{\prime }\right)=1-\frac{6}{49}=\frac{43}{49}$