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) = `("n"("B"))/("n"("S")) = 450/1000`

Number of girls studying in XI is 20% of 450 = `20/100 xx 450` = 90

i.e., n(A ∩ B) = 90

∴ P(A ∩ B) = `("n"("A" ∩ "B"))/("n"("S")) = 90/100`

We have to find P`("A"/"B")`

`"P"("A"/"B") = ("P"("A" ∩ "B"))/("P"("B")) = (90/1000)/(450/1000) = 90/450 = 1/5 = 0.2`