Question

A bag contains tickets numbered from $1$ and $20$. Two tickets are drawn. The probability that both the numbers are prime is

• A. $\frac{14}{95}$
• B. $\frac{7}{95}$
• C. $\frac{1}{95}$
• D. None of these

Answer 1

The correct option is A

$\frac{14}{95}$

Explanation for the correct option:

Find the probability:

Total number of tickets $=20$

Probability of drawing two tickets $={}^{20}C_2$

Now, there are $8$ prime numbers in between $1$ to $20$, $\left\{2,3,5,7,11,13,17,19\right\}$

Probability of favorable cases $={}^{8}C_2$

$\therefore$The required probability $=\frac{{}^{8}C_2}{{}^{20}C_2}$ $\left[\because \mathrm{Probability}=\frac{\mathrm{favourable}\mathrm{ways}}{\mathrm{total}\mathrm{ways}}\right]$

$$\begin{gathered} =\frac{28}{190} \\ =\frac{14}{95} \end{gathered}$$

Hence, Option (A) is correct.