Question

How many outcomes are there in the sample space of throwing two dice?

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Answer 1

When we throw two dice we get two numbers of the form (p, q) where p is the outcome of first die and q is the outcome of second die. p and q can be any of the six numbers 1, 2, 3, 4, 5, 6

So, all the possible combinations are

(1, 1), (1, 2) .......(1, 6)

(2, 1) (2, 2) .......(2, 6)

.

.

.

(6, 1), (6, 2) ........(6, 6)

We can see that each row has six outcomes and there are six rows.

$\Rightarrow$ There are 6 $\times$ 6 elements in the sample space.

= 36.