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NECO 2008 Mathematics · Question 30

The chances of Usman and Dele passing a Mathematics test are 3/5 and 1/3, respectively. What is the probability that neither of them passes the test?

Options

  1. A.35\frac{3}{5}
  2. B.25\frac{2}{5}
  3. C.415\frac{4}{15}
  4. D.15\frac{1}{5}
  5. E.215\frac{2}{15}

Answer: C. 415\frac{4}{15}

Explanation written with AI and checked against the answer key

Analyze the question: We want the probability that both Usman and Dele fail. We assume their results are independent.

Concept: P(neither passes) = P(Usman fails) × P(Dele fails), where P(fails) = 1 − P(passes).

Solution:

  • P(Usman fails) = 1 − 3/5 = 2/5
  • P(Dele fails) = 1 − 1/3 = 2/3

P(neither passes) = 2/5 × 2/3 = 4/15

Answer: The correct option is C, 4/15.

Tip: For "neither" or "none" questions, find the complement of each event first, then multiply. Do not multiply the pass probabilities (3/5 × 1/3 = 1/5), because that gives the probability that both pass. This is the trap option D.

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