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In a certain city 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 into advertisements and 40% of those who read B but 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 that reads an advertisement?

In a certain city 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 into advertisements and 40% of those who read B but 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 that reads an advertisement?

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
7 years ago
Hello Student,
Please find the answer to your question
KEY CONCEPT:
(Total prob. Theorem) If E1, E2, E3. . . . . . Enare mutually exclusive and exhaustive events and E is an event which can take place in conjunction with any one of E1then
P (E) = P (E1) P (EI E1) + P (E2) P (EI E2) + . . . . . . . . + P (En) P (EI En) Let P (A) denote the prob. of people reading newspaper A and P (B) that of people reading newspaper B
Then, P (A) = 25/100 = 0.25
P (B) = 20/100 = 0.20, P (AB) = 8/100 = 0.08
Prob. of people reading the newspaper A but not B = P (ABc)
= P (A) – P(AB) = 0.25 – 0.08 = 0.17
Similarly,
P (AcB) = P (B) – P (AB) = 0.20 – 0.08 = 0.12
Let E be the event that a person reads an advertisement.
Therefore
ATQ, P (EI ABc) = 30/100; P (EI AcB) = 40/100
P (EI AB) = 50/100
∴ By total prob. theorem (as ABc, AcB and AB are mutually exclusive)
P (E) = P (EI ABc) P (ABc) + P (EI AcB) P (AcB) + P (EI AB). P (AB)
= 30/100 x 0.17 + 40/100 x 0.12 + 50/100 x 0.08
= 0.051 + 0.048 + 0.04
Thus the population that reads an advertisements is 13.9%

Thanks
Jitender Pal
askIITians Faculty

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