WAEC 2016 · Paper 2 · Q12

Probability & distributions

A survey indicated that $65\%$ of the families in a town own cars. Find, correct to three decimal places, the probability that among 7 families selected at random in the town:

(a)
exactly 5 of them own cars;
(b)
3 or 4 of them own cars;
(c)
at most 2 of them own cars.

Worked solution (try it first)

$X \sim B(7, 0.65)$ , with $q = 0.35$ .

(a)

$P(X = 5)$
$= \binom75(0.65)^5(0.35)^2$
$\approx 0.298$ .

(b)

$P(3) + P(4) = 0.1442 + 0.2679$
$\approx 0.412$ .

(c)

At most 2: $P(0) + P(1) + P(2) = 0.0006 + 0.0084 + 0.0466$
$\approx 0.056$ .

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