Three newspapers A, B and C are published in a city and a survey of readers indicatesthe following: 20% read A, 16% read B, 14% read C, 8% read both A and B, 5% readboth A and C, 4% read both B and C, 2% read all the three. For a person chosen atrandom, find the probability that the person reads none of the newspapers
Question
Three newspapers A, B and C are published in a city and a survey of readers indicatesthe following: 20% read A, 16% read B, 14% read C, 8% read both A and B, 5% readboth A and C, 4% read both B and C, 2% read all the three. For a person chosen atrandom, find the probability that the person reads none of the newspapers
Solution
To find the probability that a person reads none of the newspapers, we first need to find the probability that a person reads at least one newspaper.
We know that:
P(A) = 20% = 0.20 P(B) = 16% = 0.16 P(C) = 14% = 0.14 P(A ∩ B) = 8% = 0.08 P(A ∩ C) = 5% = 0.05 P(B ∩ C) = 4% = 0.04 P(A ∩ B ∩ C) = 2% = 0.02
The probability that a person reads at least one newspaper is given by the sum of the probabilities of reading each newspaper, minus the probabilities of reading two newspapers (since we've double counted those), plus the probability of reading all three (since we've subtracted this probability three times in the previous step):
P(At least one) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
Substituting the known values gives:
P(At least one) = 0.20 + 0.16 + 0.14 - 0.08 - 0.05 - 0.04 + 0.02 = 0.35
The probability that a person reads none of the newspapers is the complement of the probability that a person reads at least one newspaper:
P(None) = 1 - P(At least one) = 1 - 0.35 = 0.65
So, the probability that a person reads none of the newspapers is 0.65 or 65%.
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