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

Options

A. `1/10`
B. `2/5`
C. `9/20`
D. `1/3`

Explanation

To solve the problem step by step, we will use the concept of conditional probability. We need to find the probability that a student fails in physics given that they have failed in mathematics.

### Step 1: Define the probabilities
Let:
- \( P(H) \) = Probability of failing in Physics = 30% = \( \frac{30}{100} = \frac{3}{10} \)
- \( P(M) \) = Probability of failing in Mathematics = 25% = \( \frac{25}{100} = \frac{5}{20} \)
- \( P(H \cap M) \) = Probability of failing in both Physics and Mathematics = 10% = \( \frac{10}{100} = \frac{1}{10} \)

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