Question

If two balanced dice are tossed once, the probability of the event, that the sum of the integers coming on the upper sides of the two dice is $9$ is

• A. $\frac{7}{18}$
• B. $\frac{5}{36}$
• C. $\frac{1}{9}$
• D. $\frac{1}{6}$

Answer 1

The correct option is C

$\frac{1}{9}$

Explanation for the correct option:

Finding the probability:

Total number of possible outcomes when two dice are tossed $=6\times 6$

Now, possible events where the sum of upper side of dice is $9$ $=\left\{\left(3,6\right)\left(4,5\right)\left(5,4\right)\left(6,3\right)\right\}$

$\therefore$Total number of possible events $=4$

$\begin{array}{rcl}\therefore \mathrm{Required}\mathrm{Probability}& =& \frac{\mathrm{Total}\mathrm{number}\mathrm{of}favourableoutcomes}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}}\\ & =& \frac{4}{6\times 6}\\ & =& \frac{4}{36}\\ & =& \frac{1}{9}\end{array}$

Hence, the correct option is C.