Question

An unbiased cubic die marked with $1,2,2,3,3,3$ is rolled $3$ times. The probability of getting a total score of $4$ or $6$ is?

• A. $\frac{16}{216}$
• B. $\frac{50}{216}$
• C. $\frac{60}{216}$
• D. None

Answer 1

The correct option is B $\frac{50}{216}$

Given the cubic die is marked with $1,2,2,3,3,3$ and rolled 3 times.

Let the event of getting a score of $4$ or $6$ be $E$

The only possible way to get $4$ is $112$

$121$

$211$

The Probability of 1 showing up is $\frac{1}{6}$

Probability of 2 showing up is $\frac{2}{6}$

Probability of 2 showing up is $\frac{3}{6}$

So, probability of scoring 4 is $\frac{1}{6}\times \frac{1}{6}\times \frac{2}{6}\times 3$

$=\frac{6}{216}$

The possible ways to get 6 are 123 and 2

$\downarrow$

total 6 ways

So, probability of scoring 6 is $\frac{1}{6}\times \frac{2}{6}\times \frac{3}{6}\times 6+\left(\frac{2}{6}\right)$

$=\frac{36+8}{216}$

$=\frac{44}{216}$

Probability of getting a total score of 4 or 6

$=\frac{6}{216}+\frac{44}{216}=\frac{50}{216}$