Question

An integer is chosen at random between $1$ to $1100$. Find the probability that is
(i) Divisible by $8$
(ii) Not divisible by $8$.

Answer 1

$1,2,3,----,1100$

Total no. that divisible by 8 are $\to \left[\frac{1100}{8}\right]=\left[137.5\right]$

$=137$

(i) P (divisible by 8) $=\left(\frac{137C_1}{1100C_1}\right)=\left(\frac{137}{1100}\right)$

(ii) P(not divisible by 8 ) $=1-\left(\frac{137}{1100}\right)=\left(\frac{963}{1100}\right)$