In a college, 30% students fail in physics, 25% fail in mathematics and 10% fail in both. One student is chosen at random. The probability that she fails in physics if she has failed in mathematics is


Let A denotes the event that students failed in physics.


According to question: 30% students failed in physics.


P(A) = 0.30


Similarly, if we denote the event of failing in maths with B.


We can write that:


P(B) = 0.25


Also, probability of failing in both subjects can be represented using intersection as shown:


P (A B) = 0.1


Now we need find a conditional probability of failing of student in physics given that she has failed in mathematics.


We can represent the situation mathematically as-


P(A|B) =?


Using the fundamental idea of conditional probability, we know that:


P(E|F) =


where E & F denotes 2 random events.


P(A|B) =


P(A|B) =


Clearly our answer matches with option B.


Option (B) is the only correct choice.

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