Question

In a class with 42 students, 22 like blue and 27 like red. If 6 no like either colours.

Find :- a) How many students like both red and blue

b) How many students like red only

c) How many students like blue only

Answer 1

Number of students who like both red and blue are 13.

Number of students who like red only = 14

Number of Students who like blue only = 9

Explanation:

Total number of students P (U) = 42

Number of students who like blue P(B) = 22

Number of students who like red P(R) = 27

Number of student who like neither red nor blue = P (B ∪ R)'

P (B ∪ R) = P(U) - P (B ∪ R)'

= 42 - 6

= 36

Now Case 1:

students who like both red and blue = P (B ∩ R)

Now using,

P( B ∪ R) = P(B) + P(R) - P (B ∩ C)

36 = 22 + 27 - P (B ∩ C)

P (B ∩ C) = 49 - 36 = 13

So the number of students who like both red and blue are 13.

Case 2:

Number of students who like red only = P (R) - P (B ∩ C)

= 27 - 13

= 14

Case 3:

Number of Students who like blue only = P(B) - P (B ∩ C)

= 22 - 13

= 9