WAEC 2019 · Paper 2 · Q8

(a)
Two fair dice are thrown together two times. Find the probability of obtaining a sum of seven in the first throw and a sum of four in the second throw.

Worked solution (try it first)

With two dice there are 36 equally likely outcomes.
A sum of 7 happens 6 ways, so $P = \frac{6}{36}$ .
A sum of 4 happens 3 ways: $(1, 3), (2, 2), (3, 1)$ , so $P = \frac{3}{36}$ .
The two throws are independent: $\frac{6}{36} \times \frac{3}{36} = \frac{18}{1296}$
$= \frac{1}{72}$ .