Question

In a school, there are $1000$ student, 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?.

Answer 1

Total number of students $=1000$

Total number of girls $=430$

Girls studying in class $XII=10\%\text{of}430$

$=\frac{10}{100}\times 430$

$=43$

We need to find the probability that a student chosen randomly studies in class $XII$, given that the chosen student is a girl.

$A$ : Student is in class $XII$

$B$ : Studenet is a girl

Therefore,

$P\left(A|B\right)$ $=\frac{P(A\cap B)}{P\left(B\right)}=\frac{\text{No. of girls studying in class XII}}{\text{Number of girls}}=\frac{43}{430}=0.1$