Question

Tickets numbered from $1$ to $30$ are mixed up and then a ticket is drawn at random. What is the probability that the drawn ticket has a number which is divisible by both $2$ and $6$?

• A. $\frac{1}{2}$
• B. $\frac{2}{5}$
• C. $\frac{8}{15}$
• D. $\frac{1}{6}$

Answer 1

The correct option is D $\frac{1}{6}$

Here, $S=\{1,2,3,4,5,6,.....29,30\}$

Let $E$ be the event of number divisible by both $2$ and $6$.

$E=\{6,12,18,24,30\}$

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{5}{30}=\frac{1}{6}$

$\therefore$ the probability that the drawn ticket has a number which is divisible by both $2$ and $6$ is $\frac{1}{6}$