Question

In a single throw of three dice, find the probability of getting the same number on the three dice.

Answer 1

Hint: To solve this question, we will start with finding the total outcomes of throwing dice three times, then we will find the favourable outcomes of throwing three dice. Afterwards using the formula, we will get the probability of getting the same number on the three dice.

Complete step-by-step answer:
We have been given, that we need to throw three dice. So, we need to find the probability of getting the same number on the three dice.
We know that, \[Probability = \dfrac{{{\text{favourable outcomes}}}}{{{\text{total outcomes}}}}\]\[ \ldots .eq.\left( 1 \right)\]
Now, outcomes of throwing single dice \[ = {\text{ }}\left\{ {1,2,3,4,5,6} \right\}{\text{ }} = {\text{ }}6\]
So, total outcomes of throwing dice three times \[ = {\text{ }}6 \times 6 \times 6{\text{ }} = {\text{ }}216\]
Now favourable outcomes of throwing three dice \[ = {\text{ }}\left\{ {1,1,1} \right\},{\text{ }}\left\{ {2,2,2} \right\},{\text{ }}\left\{ {3,3,3} \right\},{\text{ }}\left\{ {4,4,4} \right\},{\text{ }}\left\{ {5,5,5} \right\},{\text{ }}\left\{ {6,6,6} \right\}{\text{ }} = {\text{ }}6\]
On putting the value of favourable outcomes and total outcomes in \[eq.\left( 1 \right),\]we get
Probability of getting the same number on the three dice $ = \dfrac{6}{{216}}$
$ = \dfrac{1}{{36}}$
Thus, probability of getting the same number on the three dice is $\dfrac{1}{{36}}.$

Note: In probability, the number of favourable outcomes is the total number of choices we are actually looking for and total outcomes are possible outcomes available.