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.