Question

Tickets numbered from $1$ to $20$ are mixed up and a ticket is drawn at random. The probability that the ticket drawn has a number which is a multiple of $3$ or $7$ is $\frac{2}{x}$, what is the value of ${}^{\prime }{x}^{\prime }$.

Answer 1

Let $E_1$ be the event of getting a multiple of $3$ or $7$.

$P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$

Multiple of $3$ from $1$ to $20$

$3,6,9,12,15,18$

Multiple of $7$ from $1$ to $20$

$7,14$

$\therefore$ Total multiple of $3$ and $7$ from $1$ to $20$

$=8$

$\therefore P\left(E_1\right)=\frac{8}{20}=\frac{2}{5}$

This is given as $\frac{2}{x}$

$\therefore \frac{2}{5}=\frac{2}{x}$

or $x=5$