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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

- $0.5$
- $0.18$
- $0.12$
- $0.06$