Question

In a school of 500 students, 200 play a musical instrument and 100 sing in a choir, and 250 neither play an instrument nor sing in the choir. What is the probability that someone who does not play an instrument is in the choir? Give your answer as a fraction in its simplest form.

Answer 1

Given that in a school of 500 students, 200 play a musical instrument and 100 sing in a choir, and 250 neither play an instrument nor sing in the choir.

A: set define that number of students who play an instrument.

B: set define that number of students who sings choir

: set define that number of students who play and instruments and also sing a choir.

Here total no of students = 500

And no of students who does not play an instrument nor sing a choir is = 250

And no of students who either play an instrument or sing a choir is

= 500 - 250 = 250

Hence form the given data we get, n() = 250, n(A) = 200, n(B) = 100

Now we kno that that,

Venn diagram related to this problem:-

for this problem we want find the probability of this shaded region.