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WAEC 2015 Mathematics · Question 8

The probability that kebba, Ebou and Omar will hit a target are 2/3 , 3/4 and 4/5 respectively. Find the…

Question

The probability that kebba, Ebou and Omar will hit a target are 23\frac{2}{3}, 34\frac{3}{4} and 45\frac{4}{5} respectively. Find the probability that only Kebba will hit the target.

  1. A.25\frac{2}{5}
  2. B.760\frac{7}{60}
  3. C.130\frac{1}{30}
  4. D.160\frac{1}{60}

Answer: C. 130\frac{1}{30}

Explanation written with AI and checked against the answer key

Analyze the question: We need the probability that Kebba hits the target AND Ebou misses AND Omar misses. The three events are independent, so we multiply their probabilities.

Concept: For independent events, P(A and B and C) = P(A) × P(B) × P(C). The probability of missing is 1 − P(hit).

Solution:

  • P(Kebba hits) = 2/3
  • P(Ebou misses) = 1 − 3/4 = 1/4
  • P(Omar misses) = 1 − 4/5 = 1/5

P(only Kebba hits) = 2/3 × 1/4 × 1/5 = 2/60 = 1/30

Tip: For "only one person succeeds" questions, give the chosen person their success probability and give everyone else their failure probability (1 − p), then multiply. Always simplify at the end: 2/60 = 1/30. Don't confuse this with option D (1/60), which comes from forgetting the 2 in the numerator.

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