Q221 / 270 · NDA 2020 · Mathematics

In a lottery of 10 tickets numbered 1 to 10 , two tickets are drawn simultaneously. What is the probability that both the tickets drawn have prime numbers?

  • A
    $\frac{1}{15}$
  • B
    $\frac{1}{2}$
  • Correct answer
    C
    $\frac{2}{15}$
  • D
    $\frac{1}{5}$

Solution

Prime number between 1 to 10 are 2, 3, 5, 7 . Now, number of ways of selecting 2 prime number out of 4 primenumber $={ }^4 C_2=6$. Number of ways of selecting 2 numbers out of 10 numbers $={ }^{10} C_2=45$. $\therefore$ Required probability $=\frac{6}{45}=\frac{2}{15}$.

Hence, the correct answer is option: 'C'.

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