WAEC 2022 Mathematics · Question 11

A local community has two newspapers: the morning tomes and the evening dispatch. The morning times is read by…

Question

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?

A.0.45
B.0.65
C.0.85
D.0.95

Answer: C. 0.85

Explanation written with AI and checked against the answer key

Analyze the question: We need P(a household reads at least one paper), which means P(M ∪ E), the probability of reading the Morning Times or the Evening Dispatch (or both).

Concept: The addition rule for two events:

P(M ∪ E) = P(M) + P(E) − P(M ∩ E)

We subtract the overlap because households reading both papers get counted twice when we add P(M) and P(E).

Solution:

P(M) = 45% = 0.45
P(E) = 60% = 0.60
P(M ∩ E) = 20% = 0.20

P(M ∪ E) = 0.45 + 0.60 − 0.20 P(M ∪ E) = 1.05 − 0.20 P(M ∪ E) = 0.85

Check with a Venn diagram:

Both papers: 20%
Morning Times only: 45 − 20 = 25%
Evening Dispatch only: 60 − 20 = 40%
Total reading at least one: 25 + 20 + 40 = 85% ✓

Tip: "At least one" or "either...or" signals the union, so use P(A) + P(B) − P(A∩B). If your sum of the two probabilities exceeds 1 (like 1.05 here), you must subtract the overlap. Forgetting to subtract would give 1.05, which is impossible for a probability. That is a quick sign you've made a mistake.

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