WAEC 2010 · Paper 2 · Q15

(a)
A team of 3 students is to be selected from 5 boys and 4 girls to represent a school in a quiz. (i) If there is no restriction, in how many ways can the team be selected? (ii) Calculate, correct to three decimal places, the probability that there will be at least two girls in the team.
Separate values with commas, e.g. 3, −2
(b)
The probability that a player will score a penalty kick is $0.8$ . If he takes 5 penalty kicks, calculate, correct to four decimal places, the probability that he will score: (i) no goal; (ii) at most two goals.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

2 girls and 1 boy: ${}^4C_2 \times {}^5C_1 = 6 \times 5 = 30$ ways. 3 girls: ${}^4C_3 = 4$ ways.
Probability $= \dfrac{30 + 4}{84}$
$= \dfrac{34}{84}$
$\approx 0.405$ .

$P(1) = 5(0.8)(0.2)^4 = 0.0064$ and $P(2) = 10(0.8)^2(0.2)^3 = 0.0512$ .
$P(\text{at most } 2) = 0.00032 + 0.0064 + 0.0512$
$= 0.05792$
$\approx 0.0579$ .