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WAEC 2017 Mathematics · Question 15

Two bottles are drawn with replacement from a crate containing 8 Coke, 12 Fanta, and 4 Sprite bottles. What is…

Question

Two bottles are drawn with replacement from a crate containing 8 Coke, 12 Fanta, and 4 Sprite bottles. What is the probability that the first is coke and the second is not coke?

  1. A.112\frac{1}{12}
  2. B.16\frac{1}{6}
  3. C.29\frac{2}{9}
  4. D.38\frac{3}{8}

Answer: C. 29\frac{2}{9}

Explanation written with AI and checked against the answer key

Analyze the question: There are 8 + 12 + 4 = 24 bottles in total. We draw two bottles with replacement, so the two draws are independent. We want P(first is Coke AND second is not Coke).

Concept: For independent events, P(A and B) = P(A) × P(B). With replacement, the crate is restored after the first draw, so the probabilities do not change.

Solution:

  • P(first is Coke) = 8/24 = 1/3
  • P(second is not Coke) = 16/24 = 2/3 (the 12 Fanta and 4 Sprite bottles)

P = 1/3 × 2/3 = 2/9

Answer: Option C, 2/9.

Tip: In "with replacement" questions, the denominator stays the same for every draw. Also, "not Coke" is easiest as 1 − P(Coke) = 1 − 1/3 = 2/3.

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