Question

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

• A. $14/95$
• B. $7/95$
• C. $1/95$
• D. None of these

Answer 1

The correct option is A $14/95$

Prime no.'s between $1$ to $20$ are $2,3,5,7,11,13,17,19$

No. of ways of selecting $2$ of them are $8_{C_2}=\frac{8!}{6!\times 2!}=\frac{8\times 7}{2}=28$

No. of ways of selecting $2$ from $1-20$ are ${20}_{C_2}=\frac{20\times 19}{2}=190$

Probability $=\frac{28}{190}=\frac{14}{95}$.