Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that :

(i)

same number appears on both the dice ?

(ii)

different number appears on both the dice ?

Possible outcomes are

\[\begin{array}{l} (1,1)(1,2),(1,3),(1,4),(1,5),(1,6) \\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6) \\ (3,1)(3,2),(3,3),(3,4),(3,5),(3,6) \\ (4,1)(4,2),(4,3),(4,4),(4,5),(4,6) \\ (5,1),(5,2),(5,3),(5,4),(5,5),(5,6) \\ (6,1),(6,2),(6,3),(6,4),(6,5),(6,6) \end{array} \]

$\displaystyle \mathrm{P}($ same number appear on both the dice $\displaystyle )=\frac{6}{36}$ or $\displaystyle \frac{1}{6}$

P (different number appear on both the dice) $\displaystyle =1-\frac{1}{6}=\frac{5}{6}$