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WAEC 2011 · Paper 2 · Q13

A survey conducted revealed that four out of every twenty taxi drivers do not have a valid driving licence. If 6 drivers are selected at random, calculate, correct to three decimal places, the probability that:

  1. (a)

    exactly 2;

  2. (b)

    more than 3;

  3. (c)

    at least 5 have valid driving licence.

Worked solution (try it first)
  1. A success is a driver with a valid licence: q=420=0.2q = \frac{4}{20} = 0.2, so p=0.8p = 0.8, with n=6n = 6.

(a)

  1. P(X=2)P(X = 2)
    =(62)(0.8)2(0.2)4= \binom62(0.8)^2(0.2)^4
    =15×0.64×0.0016= 15 \times 0.64 \times 0.0016
    =0.01536= 0.01536
    ≈0.015\approx 0.015.

(b)

  1. More than 3 means 4, 5 or 6: P(4)=0.24576P(4) = 0.24576, P(5)=0.393216P(5) = 0.393216 and P(6)=0.262144P(6) = 0.262144.
  2. Add: 0.90112≈0.9010.90112 \approx 0.901.

(c)

  1. At least 5: P(5)+P(6)=0.393216+0.262144P(5) + P(6) = 0.393216 + 0.262144
    =0.65536= 0.65536
    ≈0.655\approx 0.655.

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