WAEC 2022 · Paper 2 · Q5

Probability & distributions

The probability that Abiola will be late to office on a given day is $\frac25$ . In a given working week of six days, find, correct to four significant figures, the probability that he will:

(a)
be late for only 3 days;
(b)
not be late in the week;
(c)
be late throughout the six days.

Worked solution (try it first)

$X \sim B\left(6, \frac25\right)$ , with $q = \frac35$ .

(a)

$P(3) = \binom63\left(\frac25\right)^3\left(\frac35\right)^3$
$= \dfrac{4320}{15625}$
$\approx 0.2765$ .

(b)

$P(0) = \left(\frac35\right)^6$
$= \dfrac{729}{15625}$
$\approx 0.04666$ .

(c)

$P(6) = \left(\frac25\right)^6$
$= \dfrac{64}{15625}$
$= 0.004096$ .

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