Question

In a lottery of $50$ tickets numbered $1$ to $50$, two tickets are drawn simultaneously. The probability that both the tickets drawn have prime numbers.

• A. $\frac{1}{35}$
• B. $\frac{16}{35}$
• C. $\frac{7}{35}$
• D. $\frac{3}{35}$

Answer 1

The correct option is D $\frac{3}{35}$

Number of prime numbers between $1$ to $50$ is $15$

So probability of getting a prime number in the first draw will be $=\frac{15}{50}$

If one card is drawn from the pack of lottery tickets.

The number of prime numbers remaining in the bunch will be $14$

Total lottery tickets remaining in the bunch $=49$

The probability of getting a prime number $\frac{14}{49}$

So, the probability of getting prime numbers in two draws $=\frac{15}{50}\times \frac{14}{49}=\frac{3}{35}$