Question

A natural number is chosen at random from amongst the first $50$. The probability that the number chosen is divisible by $3$ or $5$ is?

Answer 1

Numbers divisible by $3$ in first $50$ natural numbers$=\{3,6,9,.....48\}$

$\Rightarrow n\left(3\right)=16$

Numbers divisible by $5$ in first $50$ natural numbers$=\{5,10,15,....50\}$

$n\left(5\right)=10$

numbers divisible by both $3$ and $5=\{15,30,45\}$

$n(3\cap 5)=3$

$n(3\cup 5)=n\left(3\right)+n\left(5\right)-n(3\cap 5)$

$=16+10-3=23$

$\therefore$ Probability that a randomly drawn number is divisible by $3$ or $5$ is $\frac{n\left(3or5\right)}{50}=\frac{23}{50}$.