WAEC 2017 · Paper 2 · Q12

Probability & distributions

(a)
In a school, the ratio of those who passed to those who failed a History test is $4 : 1$ . If 7 students are selected at random from the school, find, correct to two decimal places, the probability that: (i) at least 3 students passed the test; (ii) between 3 and 6 students failed the test.
Separate values with commas, e.g. 3, −2
(b)
A fair die is thrown five times. Find the probability of obtaining a six three times.

Worked solution (try it first)

(a)

$P(\text{pass}) = \frac45 = 0.8$ , with $n = 7$ .

(i)

At least 3 passed $= 1 - [P(0) + P(1) + P(2)]$
$= 1 - 0.0047$
$= 0.9953$
$\approx 1.00$ .

(ii)

Between 3 and 6 failed means 4 or 5 failed: $\binom74(0.2)^4(0.8)^3 + \binom75(0.2)^5(0.8)^2 = 0.0287 + 0.0043$
$\approx 0.03$ .

(b)

$P(\text{six}) = \frac16$ : $\binom53\left(\frac16\right)^3\left(\frac56\right)^2 = \dfrac{250}{7776}$
$\approx 0.0322$ .

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