Question

Three dice are thrown simultaneously. What is the probability of containing a total of $17$ or $18$

• A. $\frac{1}{9}$
• B. $\frac{1}{72}$
• C. $\frac{1}{54}$
• D. None of these

Answer 1

The correct option is C

$\frac{1}{54}$

Explanation for the correct answer.

Given: Three dice are rolled

Total number of sample spaces $=6\times 6\times 6=216$

Sample space to get a sum of $17=\left\{(6,6,5),(5,6,6),(6,5,6)\right\}$

Sample space to get a sum of $18=\left\{6,6,6\right\}$

Probability $=\frac{Totalnumberoffavourableevents}{Totalpossibleevents}$

Probability of getting a sum $17=\frac{3}{216}$

Probability of getting a sum $18=\frac{1}{216}$

Probability of getting a total of $17$ or $18$ $=\frac{3}{216}+\frac{1}{216}=\frac{4}{216}=\frac{1}{54}$

Hence option C is the correct answer.