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WAEC 2022 · Paper 2 · Q13

A soldier fires at a target and the probability of hitting the target with any shot is 25\frac25. If he fires 6 shots, find, correct to three decimal places, the probability that he hits the target:

  1. (a)

    6 times;

  2. (b)

    at most 3 times;

  3. (c)

    at least 2 times.

Worked solution (try it first)
  1. X∼B(6,25)X \sim B\left(6, \frac25\right).
  2. Over 15 625: P(0)=729P(0) = 729, P(1)=2916P(1) = 2916, P(2)=4860P(2) = 4860, P(3)=4320P(3) = 4320.

(a)

  1. P(6)=(25)6P(6) = \left(\frac25\right)^6
    =6415625= \dfrac{64}{15625}
    ≈0.004\approx 0.004.

(b)

  1. At most 3: 729+2916+4860+432015625=1282515625\dfrac{729 + 2916 + 4860 + 4320}{15625} = \dfrac{12825}{15625}
    ≈0.821\approx 0.821.

(c)

  1. At least 2: 1−729+291615625=11980156251 - \dfrac{729 + 2916}{15625} = \dfrac{11980}{15625}
    ≈0.767\approx 0.767.

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