Question

There are 1000 students in a school out of which 450 are girls. It is known that out of 450, 20% of the girls studying in class XI. A student is randomly selected from 1000 students. What is the probability that the selected student is from class XI given that the selected student is a girl?

Answer 1

Number of students = 1000 i.e., n(S) = 1000 

Let A be the event of selecting a girl student from class XI. 

Let B be the event of selecting a girl student 

Number of girls = 450; n(B) = 450

∴ P(B) = \(\frac{n(B)}{n(S)}=\frac{450}{1000}\)

Number of girls studying in XI is 20% of 450 = \(\frac{20}{100}\) x 450 

= 90 

i.e., n(A ∩ B) = 90 

∴ P(A ∩ B) = \(\frac{n(A∩B)}{n(S)}=\frac{90}{1000}\)

We have to find P(\(\frac{A}{B}\))