Question

Two dice are thrown simultaneously. What is the probability of not getting same numbers on both dice?

Answer 1

Let us make a table to show all possible outcomes

$$\begin{array}{ccccccc}& \text{1}& \text{2}& \text{3}& \text{4}& \text{5}& \text{6}\\ 1& 1,1& 1,2& 1,3& 1,4& 1,5& 1,6\\ 2& 2,1& 2,2& 2,3& 2,4& 2,5& 2,6\\ 3& 3,1& 3,2& 3,3& 3,4& 3,5& 3,6\\ 4& 4,1& 4,2& 4,3& 4,4& 4,5& 4,6\\ 5& 5,1& 5,2& 5,3& 5,4& 5,5& 5,6\\ 6& 6,1& 6,2& 6,3& 6,4& 6,5& 6,6\end{array}$$

P(getting same numbers) $=\frac{\text{Outcome having same numbers}}{\text{Total Outcomes}}=\frac{6}{36}=\frac{1}{6}$

P(not getting same numbers) = 1- $\frac{1}{6}$ = $\frac{5}{6}$