WAEC 2013 · Paper 2 · Q15

(a)
The probability that a man wins a race is 0.8. In four different races, what is the probability that he wins: (i) all races; (ii) no race; (iii) at most 3 races?
Separate values with commas, e.g. 3, −2
(b)
A class consists of 5 girls and 10 boys. If a committee of 5 is chosen at random from the class, find the probability that: (i) 3 boys are selected; (ii) at least one girl is selected.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

(a)(i)

Winning each race is independent: $P(\text{all 4}) = 0.8^4 = 0.4096$ .

(ii)

$P(\text{none}) = 0.2^4 = 0.0016$ .

(iii)

At most 3 is everything except winning all 4: $1 - 0.4096 = 0.5904$ .

(b)

There are $\,{}^{15}C_5 = 3003$ committees.

(i)

3 boys and 2 girls: $\,{}^{10}C_3 \times {}^5C_2 = 120 \times 10$
$= 1200$ , so $P = \dfrac{1200}{3003} \approx 0.3996$ .

(ii)

At least one girl is everything except all boys: $1 - \dfrac{{}^{10}C_5}{3003} = 1 - \dfrac{252}{3003}$
$\approx 0.9161$ .

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