Question

If three dice are thrown simultaneously, then the probability of getting a score of $7$ is

• A. $\frac{5}{216}$
• B. $\frac{1}{6}$
• C. $\frac{5}{72}$
• D. None of these

Answer 1

The correct option is C

$\frac{5}{72}$

Explanation for the correct option:

Finding the probability:

If the Three dice are thrown simultaneously, the total number of outcomes $\begin{array}{rcl}& =& 6^3\end{array}$

The possible outcomes of getting a score $7$,

$$\begin{gathered} =\left\{\left(1,1,5\right)\left(1,5,1\right)\left(5,1,1\right)\left(2,2,3\right)\left(2,3,2\right)\left(3,2,2\right)\left(3,3,1\right)\left(3,1,3\right)\left(1,3,3\right)\left(4,2,1\right)\left(1,4,2\right)\left(2,1,4\right)\left(1,2,4\right)\left(2,4,1\right)\left(4,1,2\right)\right\} \\ =15 \end{gathered}$$

Therefore,

$\begin{array}{rcl}\mathrm{P}\left(\mathrm{getting}\mathrm{a}\mathrm{score}\mathrm{of}7\right)& =& \frac{\mathrm{Total}\mathrm{possible}\mathrm{outcomes}\mathrm{to}\mathrm{get}7}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}\\ & =& \frac{15}{6^3}\\ & =& \frac{15}{216}\\ & =& \frac{5}{72}\end{array}$

Hence, the correct option is C.