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WAEC 2014 · Paper 2 · Q13

  1. (a)

    A fair coin is tossed four times. Calculate the probability of obtaining: (i) at least one head; (ii) an equal number of heads and tails.

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

  2. (b)

    The probabilities that Sani, Kalu and Tato will hit a target are 34\frac34, 25\frac25 and 13\frac13 respectively. If all three men shoot once, what is the probability that the target will be hit only once?

Worked solution (try it first)

(a)(i)

  1. At least one head is everything except four tails: 1−(12)4=15161 - \left(\frac12\right)^4 = \frac{15}{16}.

(ii)

  1. Two heads and two tails: (42)(12)4=616\binom42\left(\frac12\right)^4 = \frac{6}{16}
    =38= \frac38.

(b)

  1. The miss chances are 14\frac14, 35\frac35 and 23\frac23.
  2. Only Sani: 34⋅35⋅23=1860\frac34 \cdot \frac35 \cdot \frac23 = \frac{18}{60}.
  3. Only Kalu: 14⋅25⋅23=460\frac14 \cdot \frac25 \cdot \frac23 = \frac{4}{60}.
  4. Only Tato: 14⋅35⋅13=360\frac14 \cdot \frac35 \cdot \frac13 = \frac{3}{60}.
  5. Add: 2560=512\frac{25}{60} = \frac{5}{12}.

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