The probability of men getting a certain disease is $\frac{1}{2}$ and that of women getting the same disease is $\frac{1}{5}.$ The blood test that identifies the disease gives the correct result with probability $\frac{4}{5}$. Suppose a person is chosen at random from a group of $30$ males and $20$ females, and the blood test of that person is found to be positive. What is the probability that the chosen person is a man?

• Correct answer
  A

  $\frac{75}{107}$
• B

  $\frac{3}{5}$
• C

  $\frac{15}{19}$
• D

  $\frac{3}{10}$

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