In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, $10\%$ of the girls study in class XII. What is the probability that a student chosen randomly studies in Class XII given that the chosen student is a girl?

$0.10$

The correct answer is Option (3) → $0.10$ ##

Let $E$ denote the event that a student chosen randomly studies in Class XII and $F$ be the event that the randomly chosen student is a girl. We have to find $P(E|F)$.

Now $P(F) = \frac{430}{1000} = 0.43$ and $P(E \cap F) = \frac{43}{1000} = 0.043 \quad (\text{Why?})$

Then $P(E|F) = \frac{P(E \cap F)}{P(F)} = \frac{0.043}{0.43} = 0.1$