A local community has two newspapers: the morning tomes and the evening dispatch. The morning times is read by 45% of the households. The Evening Dispatch i...

A local community has two newspapers: the morning tomes and the evening dispatch. The morning times is read by 45% of the households.  The Evening Dispatch is read by 60% of the households.  Twenty percent of the households read both papers.  What is the probability that a particular household reads at least one paper?

Answer Details

To find the probability that a household reads at least one paper, we need to add the probabilities of households that read the Morning Times and those that read the Evening Dispatch, and then subtract the probability of households that read both papers since they are being counted twice. Let's use the following notation: - M = the event that a household reads the Morning Times - E = the event that a household reads the Evening Dispatch We are given that: - P(M) = 0.45 (45% of households read the Morning Times) - P(E) = 0.60 (60% of households read the Evening Dispatch) - P(M ∩ E) = 0.20 (20% of households read both papers) To find the probability that a household reads at least one paper, we can use the formula: P(M ∪ E) = P(M) + P(E) - P(M ∩ E) Substituting the values we have: P(M ∪ E) = 0.45 + 0.60 - 0.20 P(M ∪ E) = 0.85 Therefore, the probability that a particular household reads at least one paper is 0.85 or 85%.