Question

Compare the chances of throwing $4$ with one die$,$ $8$ with two dice$,$ and $12$ with three dice.

Answer 1

Chances of throwing $4$ with one die$=\frac{1}{6}$
Chances of throwing with $8$ with two die$=\frac{Expected}{total}$
Expected$=(2,6),(3,5),(4,4),(5,3),(6,2)$
Total$=36$
Probability$=\frac{5}{36}$
Chances of throwing $12$ with three die$=\frac{25}{216}$
Since,Expected$=25$
and Total$=6^n\Rightarrow 216$
On comparing$\frac{1}{6}:\frac{5}{36}:\frac{25}{216}$