Question

In a certain city, three newspapers A, B, and C are published. Suppose that 60% of the families in the city subscribe to newspaper A, 40% of the families subscribe to newspaper B, and 30% subscribe to newspaper C. Suppose also that 20% of the families subscribe to both A and B, 10% subscribe to both A and C, 20% subscribe to both B and C, and 5% subscribe to all three newspapers. (i) What percentage of the families in the city subscribe to at least one of the three newspapers? (ii)What percentage of the families in the city subscribe to exactly one newspaper?

Answer 1

Answer:

(i) = 85‬%

(ii) = 30%

Step-by-step explanation:

The question is a probability question.

We will need the following values:

P(A) = 60%

P(B) = 40%

P(C) = 30%

P(AnB) = 20%

p(AnC) = 10%

P(BnC) = 20%

P(AnBnC) = 5%

(i) To determine the percentage of the families in the city that subscribe to at least one of the three newspapers:

P(A) + P(B) + P(C) + P(AnBnC) - P(AnB) - p(AnC) - P(BnC)

= 60% + 40% + 30% + 5% - 20% - 10% - 20%

= 85‬%

(ii) To determine the percentage of the families in the city that subscribe to exactly one newspaper:

P(at least one paper) - p(AnB) - p(AnC) - P(BnC) -  P(AnBnC)

= 85‬% - 20% - 10% - 20% - 5%

= 30%