$A$ student answers a multiple choice question with $5$ alternatives, of which exactly $1$ is correct. The probability that he knows the correct answer is $p$, where $0 < p < 1$. If he does not know the correct answer, he randomly ticks $1$ answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly is:

• A
  $\frac{3 p}{4 p + 3}$
• B
  $\frac{5 p}{3 p + 2}$
• C
  $\frac{5 p}{4 p + 1}$
• D
  $\frac{4 p}{3 p + 1}$