Question

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
(A) 0.5 (B) 0.18
(C) 0.12 (D) 0.06

Answer 1

0.3+0.2=0.5
soA is the answer
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Answer 2

Given that a student has failed in paper2 , the probability of failing in paper1 is 0.6.

First of all, it is a conditional probability.

and given that P(F1 ∣ F2) = 0.6 ,P(F1) =.3 ,P(F2) =.2

By conditional Probability

P(F1 ∩ F2) = P(F2) .P(F1 ∣ F2) = .2 * .6 =0.12