Question

Two dice are thrown at the same time.

Find the probability of getting same number on both dice.

Answer 1

Solve for the required probability:

We know that probability of an event $P\left(E\right)=\frac{n\left(E\right)}{n\left(s\right)}$ ;where $n\left(E\right)$ and $n\left(s\right)$ are the number of favorable outcomes and total possible number of outcomes respectively.

Given that two dice are thrown $\Rightarrow n\left(s\right)=6^2=36$ ;[since a dice has $6$ faces]

Favorable outcomes are $\left(1,1\right),\left(2,2\right),\left(3,3\right),\left(4,4\right),\left(5,5\right),\left(6,6\right)\Rightarrow n\left(E\right)=6$

$\therefore$Required probability $P\left(E\right)=\frac{n\left(E\right)}{n\left(s\right)}$

$\begin{array}{cc}=& \frac{6}{36}\\ =& \frac{1}{6}\end{array}$

Hence, the required probability is $\frac{1}{6}$