Question

If a fair $6-$sided die is rolled three times$,$ what is the probability that exactly one $3$ is rolled$?$

Answer 1

Total ways in which a $6$sided die can be rolled three times $=6\times 6\times 6=216$

to get exactly one $3,$ there are three ways$;$

A $3$ on the first roll and non $3$ on other two rolls$.$ This can be done in $1\times 5\times 5=25$ ways$.$

The $3$ could be on the second or third roll too$.$ So total favorable cases$=25\times 3=75$

Required probability $\frac{75}{216}=\frac{25}{72}$