2. Three newspapers, denoted A, B and C are published in a city. A comprehensive

Question

2. Three newspapers, denoted A, B and C are published in a city. A comprehensive survey indicates that amongst the adult population of the city, 20% read A, 16% read B and 14% read C, but the survey also reveals that 8% read both A and B, 5% read both A and C, and 4% read both B and C, and that 2% read all three newspapers. A person is selected at random from the adult population of the city (that is, all adults are equally likely to be selected). Use formal notation to express the following events in terms of A, B, C, and find their probabilities. (a) the selected person reads none of the newspapers; (b) the selected person reads precisely one of the newspapers (c) the selected person reads at least A and B, given that they read at least one newspaper. 2 MARKS 2 MARKS 4 MARKS Hint: it might help to imagine a city of 100000 adults.

Explanation / Answer

from above:

a)

P(read none of newspaper)=1-P(read none) =1-0.35 =0.65

b)

c)

P(P(reads at least one and read A and B) =P(A n B) =0.08

hence probability that read at least A and B given read one newspaeper

=P(A n B)/P(A u B u C) =0.08/0.35=8/35=0.2286

P(A)= 0.2 P(B)= 0.16 P(C)= 0.14 P(AnB)= 0.08 P(BnC)= 0.04 P(AnC)= 0.05

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