91Ó°ÊÓ

Three balanced dice are rolled.

Rolling die results in 6 possible outcomes.

So, rolling three balanced dice results in\({6^3} = 216\)possible outcomes.

The possible combinations showing all the three numbers will be the same are:

\(\left( {1,1,1} \right),\left( {2,2,2} \right),\left( {3,3,3} \right),\left( {4,4,4} \right),\left( {5,5,5} \right),\left( {6,6,6} \right)\)

That is, the possible number of outcomes showing all the three numbers will be the same = 6 outcomes.

According to the classical definition of Probability, the Probability of any event E is given by:

\({\bf{P}}\left( {\bf{E}} \right){\bf{ = }}\frac{{{\bf{Number of favorable outcomes}}}}{{{\bf{Total number of outcomes}}}}\)

So, the Probability that all three numbers will be the same is obtained as:

\(\begin{aligned}{}P\left( {{\rm{all three numbers are same}}} \right) = \frac{6}{{216}}\\ = \frac{1}{{36}}\end{aligned}\)

Therefore, the required Probability is\(\frac{1}{{36}}\).