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

$\text{Probability of failing in paper 1 is} \hspace{1cm} P(A) = 0.3 \\ \text{Possibility of failing in paper 2 is} \hspace{1cm} P(B) = 0.2 \\ Probability of failing in paper 1, when \\ \text{Student has failed in paper 2 is} \hspace{1cm} P(\frac{A}{B}) = 0.6 \\ \text{We know that} \\ P(\frac{A}{B}) = \frac{(P \cap B)}{P(B)} \\ or \hspace{1cm} P(A \cap B) = P(B) P (\frac{A}{B}) = 0.6 \times 0.2 = 0.12$