A small community of 500 people isserved by two newspapers, the Chronicle and th
ID: 2953175 • Letter: A
Question
A small community of 500 people isserved by two newspapers, the Chronicle and the Sentinel. Anexamination of current subscription records show that 37% of thepeople in the community subscribe to the Chronicle and 28% of thepeople subscribe to the Sentinel. 10% of the people in thecommunity subscribe to both papers. Find the probability that aperson selected from the community at random:
a. Only reads one newspaper.
b. Doesn’t read anynewspaper.
Explanation / Answer
Let A be the event that a person subscribes to the Chronicle. Let B be the event that a person subscribes to the Sentinel. P(A) = 0.37 P(B) = 0.28 P(AB) = 0.1 (a) Only reads one newspaper --> meaning (A or B) happens butnot (A and B) P(AB) - P(AB) = P(A) + P(B) - 2P(AB) = 0.37 +0.28 - 2*0.1 = 0.45 (b) Doesn’t read any newspaper. --> Not(A or B) P(A'B') = 1 - P(AB) = 1 - [ P(A) + P(B) -P(AB)] = 1 - 0.55 = 0.45