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

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

Step-by-step 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