Question

In three throws with a pair of dice, find the chance of throwing doublets at least once.

Answer 1

No. of doublets$[(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)]$
Total no. of ways$=6^2=36$
Chance of doublet in throw$=\frac{6}{36}=\frac{1}{6}$
Chance of no. of obtaining doublet in throw$=1-\frac{1}{6}$
Chance of no. of obtaining doublet in three throws$=\frac{5}{6}$
Chance of getting doublet atleast once in three throws$={\left(\frac{5}{6}\right)}^3$
$\Rightarrow 1-{\left(\frac{5}{6}\right)}^3$
$\Rightarrow \frac{91}{216}$