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WAEC 2019 · Paper 2 · Q13

  1. (a)

    In a bakery, 30%30\% of loaves of bread produced are of bad quality. If twelve loaves are selected at random from the bakery, calculate, correct to four decimal places, the probability of getting: (i) exactly 6 bad ones; (ii) at least 4 bad ones; (iii) no bad one.

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

  2. (b)

    A group consists of 8 boys and 5 girls. A committee of 7 members is chosen from the group. Find the probability that the committee is made up of 4 boys and 3 girls.

Worked solution (try it first)

(a)

  1. X∼B(12,0.3)X \sim B(12, 0.3).

(i)

  1. P(X=6)P(X = 6)
    =12C6(0.3)6(0.7)6= {}^{12}C_6(0.3)^6(0.7)^6
    ≈0.0792\approx 0.0792.

(ii)

  1. P(X≥4)=1−[P(0)+P(1)+P(2)+P(3)]P(X \ge 4) = 1 - [P(0) + P(1) + P(2) + P(3)]
    =1−(0.0138+0.0712+0.1678+0.2397)= 1 - (0.0138 + 0.0712 + 0.1678 + 0.2397)
    ≈0.5075\approx 0.5075.

(iii)

  1. P(X=0)=0.712≈0.0138P(X = 0) = 0.7^{12} \approx 0.0138.

(b)

  1. There are  13C7=1716\,{}^{13}C_7 = 1716 committees. 4 boys and 3 girls:  8C4×5C3=70×10\,{}^8C_4 \times {}^5C_3 = 70 \times 10
    =700= 700.
  2. So P=7001716P = \dfrac{700}{1716}
    =175429= \dfrac{175}{429}
    ≈0.4079\approx 0.4079.

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