Let $X$ and $Y$ be two students who have appeared NEST. Given that i. the probability that X qualifies NEST is $\frac{1}{10}$; ii. the probability that X qualifies NEST given that Y qualifies NEST is $\frac{1}{2}$; iii. the probability that Y qualifies NEST given that X qualifies NEST is $\frac{1}{4}$. Then the probability that X does not qualify NEST given that Y does not qualify NEST is

• Correct answer
  A

  $\frac{35}{38}$
• B

  $\frac{1}{2}$
• C

  $\frac{9}{10}$
• D

  $\frac{3}{4}$

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