In a certain city only two newspapers A and B are published, it is known that `25%` of the city population reads A and `20%` reads B, while `8%` reads both A and B. It is also known that 30% of those who read A but not B look int advertisements and 40% of those who read B bu not A look into advertisements while 50% of those who read both A and B look into advertisements What is the percentage of the population reads an advertisement? [1984]

Explanation

Let P(A) and P(B) be the probability of the population in a city who read newspapers A and B, respectively. Therefore, P(A) = 25/100 = 1/4, P(B) = 20/100 = 1/5 and `P(A nn B) = 8//100` = 2/25.
Therefore, probability of those who read A but not B is
`P(A nn barB)=P(A) - P(A nn B)`
`= 1//4 - 2//25`
`= 17//100`
Similarly,
`P(B nn barA) = P(B) - P(A nn B) = 3//25`
Therefore, percentage of those who read advertisements is = 30% of `P(A nn barB) + 40% " of "P(B nn barA) + 50% " of "P(A nn B)`
`= (30)/(100) xx (17)/(100) + (40)/(100) xx (3)/(25) + (50)/(100) xx (2)/(25) = (139)/(1000)`
Hence, the percentage of the population who read an advertisement is 13.9%.