Question

Two unbiased dice are rolled. The number of elements in the sample space of the above experiment will be $\underset{–}{}$___

Answer 1

When we roll two dice and want to write the sample space of the experiment, then we are looking for all possible combinations of numbers the two dice will show. Let’s do it in a systematic way. Let’s say first dice shows 1. Then what are the possible combinations with 1 on the first dice? It will be like this
$\begin{array}{cc}Firstdice& Seconddice\\ 1& 1\\ 1& 2\\ 1& 3\\ 1& 4\\ 1& 5\\ 1& 6\end{array}$
So there are six combinations possible viz… (1,1), (1, 2), (1, 3), (1,4), (1, 5) ,(1, 6)
Similarly if first dice shows 2 again there are six possible combinations viz… (2, 1), (2, 2) (2, 3) (2, 4), (2, 5), (2, 6).
So for each number on the first dice there are six possible combinations.
For six numbers there will be 6 x 6 = 36 such combinations. Which is the correct answer.
Note: Please note that when number of elements in a sample space is large, you should first try and observe if there is some pattern involved there which repeats itself. Only when you can’t find any pattern you should go for counting all of them.