TITLE: On the probability of getting the same number for three dice
QUESTION [14 upvotes]: I found the probability of having the same number when throwing 3 dice to be $1\times\left(\frac16\right)^2$.
In addition, I don't understand how do people get the equation $\left(\frac16\right)^3\times6=\frac1{36}$, like why do we have to multiply $\left(\frac16\right)^3$ by six?

REPLY [5 votes]: Just a small supplement to the nice answers addressing your question, since I didn't found it mentioned explicitly.

We can calculate the probability of an event by calculating the ratio of the number of favorable choices or number of successes of an event with the number of all choices of an event.
This way we obtain
  \begin{align*}
\frac{\text{number of successes}}{\text{number of all choices}}=\frac{6}{6^3}=\frac{1}{6^2}=\frac{1}{36}
\end{align*}