A die is thrown twice. Find the probability that the sum of the numbers of the two faces is divisible by 4 or 5. 

Here, S = {(l, 1), (1, 2), (1, 3), ... , (6, 6)} 

Let A be the event, where the sum of the numbers of two faces is divisible by 4

= {(l, 3), (3, 1), (2, 2), (2, 6), (6, 2) 

(3, 5), (5, 3), (4, 4), (6, 6)} 

Let B be the event, where the sum of the numbers of two faces is divisible by 5. 

= {(1, 4), (4, 1), (2, 3), (3, 2), (4, 6), (6, 4), (5, 5)} 

Clearly A and B are mutually exclusive events. Thus, the required probability 

$\begin{array}{l}\Rightarrow P(A\cup B)=P\left(A\right)+P\left(B\right)\\ =\frac{9}{36}+\frac{7}{36}=\frac{16}{36}=\frac{4}{9}\end{array}$