SOLUTION: A survey of club membership of students, it is found that: 50% belongs to Club A, 55% belong to Club B, 60% belong to Club C, 30% belong to Club A and B, 25% belong to Club B and

Part A)

Belong to A ∩ B, but not C:  P ((AB) \ ABC) = 30% - 5% = 25%.


Belong to A ∩ C, but not B:  P ((AC) \ ABC) = 20% - 5% = 15%.


Belong to B ∩ C, but not A:  P ((BC) \ ABC) = 25% - 5% = 20%.


Now  the answer to question A)  is the sum  25% + 15% + 20% = 60%.    ANSWER

Part B)

Apply the inclusion-exclusion principle


    P(A U B U C) = P(A) + P(B) + P(C) - P(AB) - P(AC) - P(BC) + P(ABC) =

                 = 50%  + 55%  + 60%  - 30%   - 20%   - 25%   + 5% = 95%.


THEREFORE, the remaining 5% do not belong any club.     ANSWER