Question

What is the total number of elementary events associated with the random experiment of throwing three dice together?

Answer 1

At first, we need to find out what are the number of elementary events for a single die getting rolled. It is six. For two dice involved, for each event of the first die, there will be six corresponding events of the second die. The total number of elementary events of two dice will then be $6\times 6=36$ . Now, for each of these $36$ events, there will be six corresponding events of the third die. The total number of elementary events of three dice will then be found easily.

Complete step by step solution:
A die is a cubical shaped object with six faces. On its faces are marked the numbers $1$ to $6$ , one number on a face in a random or coordinated fashion as the case may be. The elementary event will be the event of any face showing up on rolling the die. The number of associated elementary events will then be equal to the number of faces on the die, which is six.
The scenario becomes a little tricky if three instead of one die is involved. Let us consider the experiment where three dice are rolled simultaneously. The number of elementary events for each die will be six. Now, for each event of the first die, there will be six corresponding events of the second die. The total number of elementary events of two dice will then be $6\times 6=36$ . Now, for each of these $36$ events, there will be six corresponding events of the third die. The total number of elementary events of three dice will then be $36\times 6=216$ .
Thus, we can conclude that the total number of elementary events associated with the random experiment of throwing three dice together will be $216$ .

Note: We can draw another conclusion from the above observation that there is a pattern associated with the answer for different numbers of dice. For example, for one die, we get $6$ , for two dice we get $36$ and for three dice we get $216$ . So, for “n” number of dice, we will get ${{6}^{n}}$ number of total elementary events.