Respuesta :
Answer:
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
