An examination consists of two papers, Paper1 and Paper2. The probability of failing in paper1is 0.3 and that in paper 2 is 0.2. Given that a student has failed in paper2, the probability of failingin paper1 is 0.6. Find the probability of a student failing in both the papers.
Question
An examination consists of two papers, Paper1 and Paper2. The probability of failing in paper1is 0.3 and that in paper 2 is 0.2. Given that a student has failed in paper2, the probability of failingin paper1 is 0.6. Find the probability of a student failing in both the papers.
Solution
The problem can be solved using the concept of conditional probability.
The probability of failing in Paper 1 is denoted as P(F1) = 0.3 The probability of failing in Paper 2 is denoted as P(F2) = 0.2 The probability of failing in Paper 1 given that the student has already failed in Paper 2 is denoted as P(F1|F2) = 0.6
We are asked to find the probability of a student failing in both papers, which is denoted as P(F1 ∩ F2).
According to the definition of conditional probability, we have:
P(F1|F2) = P(F1 ∩ F2) / P(F2)
We can rearrange this equation to solve for P(F1 ∩ F2):
P(F1 ∩ F2) = P(F1|F2) * P(F2)
Substituting the given values:
P(F1 ∩ F2) = 0.6 * 0.2 = 0.12
So, the probability of a student failing in both papers is 0.12 or 12%.
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