WAEC 2017 · Paper 2 · Q5

(a)
Bottles of the same size produced in a factory are packed in boxes. Each box contains 10 bottles. If $8\%$ of the bottles produced are defective, find, correct to two decimal places, the probability that a box chosen at random contains at least three defective bottles.

Worked solution (try it first)

$X \sim B(10, 0.08)$ , where $8\% = 0.08$ .
$P(0) = 0.92^{10} \approx 0.4344$ , $P(1) = 10(0.08)(0.92)^9 \approx 0.3777$ and $P(2) = 45(0.08)^2(0.92)^8 \approx 0.1478$ .
$P(X \ge 3) = 1 - 0.9599$
$= 0.0401$
$\approx 0.04$ .