Question

A number is selected at random from first $50$ natural numbers. Find the probability that it is a multiple of $3$ and $4.$

Answer 1

Here,
$s=\{1,2,3.....,50\}$

Total outcomes, $n\left(s\right)=50$

$A=$ multiples of $3=\{3,6,9,.....,48\}$

$B=$ multiples of $4=\{4,8,12,.....,48\}$

$A\cap B=$ multiples of $3\&4=\{12,24,36,48\}$

$n\left(A\right)=16$

$n\left(B\right)=12$

$n(A\cap B)=4$

Now, $P(A\cap B)=\frac{n(A\cap B)}{n\left(s\right)}=\frac{4}{50}=\frac{2}{25}$