SOLUTION: Three newspapers A, B and C are published in a certain city. It is estimated from a survey that of the adult population : 20% read A, 16% read B, 14% read C, 8% read both A and

Question 1116804: Three newspapers A, B and C are published in
a certain city. It is estimated from a survey
that of the adult population : 20% read A,
16% read B, 14% read C, 8% read both A and
B, 5% read both A and C, 4% read both B and
C, 2% read all three. Find what percentage
read at least one of the newspapers?

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

The percentage read at least one of the newspapers = (0.2 + 0.16 + 0.14 - 0.08 - 0.05 - 0.04 + 0.02)*100 = 35%.


    The first approximation is to add 20%, 16% and 14%.   (1) 


    But in this way we count elements/(readers) in each intersection  AB, AC and AB twice.


    Therefore, we subtract 8%, 5% and 4%.                 (2)


    But in this way, we loose everything/(everybody) in the intersection ABC  (because we counted it/(them) thrice first in the step (1), 

    and then excluded it/(them) thrice in the step (2). )


    Therefore, we add 2% as the last correction step.

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- Counting elements in sub-sets of a given finite set
- Advanced problems on counting elements in sub-sets of a given finite set
in this site.

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