Question

Cards with number $2$ to $101$ are placed in a box. A card is selected at random.
Find the probability that the card is
multiple of $5$.

Answer 1

Multiples of $5:5,10,15,...\dots .,100$

$\Rightarrow$ AP with first term, $a=5$, common difference $d=5$

$n^{th}$ term, $a_n=a+(n-1)d=100$

$\Rightarrow 5+(n-1)5=100$

$\Rightarrow 1+n-1=20$

$\Rightarrow n=20$

$\Rightarrow$ Probability $=\frac{20}{100}=\frac{1}{5}$ $\left(\frac{cardswithmultiplesof5}{Totalcards}\right)$.