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WAEC 2017 · Paper 2 · Q13

  1. (a)

    A bag contains 10 identical balls of which 3 are black and the rest brown. Two balls are drawn at random one after the other from the bag without replacement. Find, correct to three decimal places, the probability that both balls are of the same colour.

  2. (b)

    A multiple choice test consists of twelve questions. Each question has four possible answers of which only one is correct. A candidate answers all the questions by guessing. Find, correct to three decimal places, the probability that she gets: (i) exactly 3 correct answers; (ii) at most 8 wrong answers.

    Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)

  1. Both black: 310×29=690\dfrac{3}{10} \times \dfrac{2}{9} = \dfrac{6}{90}.
  2. Both brown: 710×69=4290\dfrac{7}{10} \times \dfrac{6}{9} = \dfrac{42}{90}.
  3. Same colour: 6+4290=815\dfrac{6 + 42}{90} = \dfrac{8}{15}
    ≈0.533\approx 0.533.

(b)

  1. Each guess is correct with p=14p = \frac14, and there are n=12n = 12 questions.

(i)

  1. P(3 correct)=12C3(14)3(34)9P(3 \text{ correct}) = {}^{12}C_3\left(\frac14\right)^3\left(\frac34\right)^9
    ≈0.258\approx 0.258.

(ii)

  1. At most 8 wrong means at least 4 correct: 1−[P(0)+P(1)+P(2)+P(3)]1 - [P(0) + P(1) + P(2) + P(3)].
  2. =1−(0.0317+0.1267+0.2323+0.2581)= 1 - (0.0317 + 0.1267 + 0.2323 + 0.2581)
    ≈0.351\approx 0.351.

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