Question

Two dice are thrown and it is known that the first die shows a 6. Find the probability that the sum of the numbers showing on two dice is 7.

Answer 1

Consider the given events.
A = First die shows 6
B = The sum of the numbers on two dice is 7.

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

$$\begin{gathered} \mathrm{Now}, \\ A\cap B=\left\{\left(6,1\right)\right\} \\ \therefore \mathrm{Required}\mathrm{probability}=P\left(B/A\right)=\frac{n\left(A\cap B\right)}{n\left(A\right)}=\frac{1}{6} \end{gathered}$$