Question

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event 'the sum of numbers on the dice is 4'.

Answer 1

Consider the given events
A = Numbers appearing on two dice are different
B = The sum of the numbers on two dice is 4

Clearly,
A = {(1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
(2, 1), (2, 3), (2, 4), (2, 5), (2, 6),
(3, 1), (3, 2), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 5), (4, 6),
(5, 1), (5, 2), (5, 3), (5, 4), (5, 6),
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5)}
B = {(1, 3), (3, 1) and (2, 2)}

$$\begin{gathered} \mathrm{Now}, \\ A\cap B=\left\{\left(1,3\right)\mathrm{and}\left(3,1\right)\right\} \\ \therefore \mathrm{Required}\mathrm{probability}=P\left(B/A\right)=\frac{n\left(A\cap B\right)}{n\left(A\right)}=\frac{2}{30}=\frac{1}{15} \end{gathered}$$