Question

A die marked with numbers $1,2,2,3,3,3$ is rolled three times. Find the probability of occurrence of $1,2$ and $3$ respectively

• A. $1/12$
• B. $1/6$
• C. $1/36$
• D. $1/24$

Answer 1

Answer: (C)

$1/36$

Given,
A Die marked with faces $1,2,2,3,3,3$ and it is rolled $3$ times.
The total no. of outcomes when a die rolled $3$ times, $N=6\times 6\times 6=216$
The total no. of outcomes to get $1,2,3$ on first,second and third roll$,X=1C_1\ast 2C_1\ast 3C_1=6$ (since no.of ways for $1$ to come on first die=$1C_1$,no. of ways for $2$ to come on second die=$2C_1$, no. of ways for $3$ to come on third die=$3C_1$)
The required probability$=\frac{X}{N}=\frac{6}{216}=\frac{1}{36}$