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An examination consists of two papers, Paper $1$ and Paper $2.$ The probability of failing in Paper $1$ is $0.3$ and that in Paper $2$ is $0.2$. Given that a student has failed in Paper $2,$ the probability of failing in Paper $1$ is $0.6$. The probability of a student failing in both the papers is

  1. $0.5$
  2. $0.18$
  3. $0.12$
  4. $0.06$

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