Question

The probability of throwing $16$ in one throw with three dice is

• A. $\frac{1}{36}$
• B. $\frac{1}{18}$
• C. $\frac{1}{72}$
• D. $\frac{1}{9}$

Answer 1

The correct option is A

$\frac{1}{36}$

Explanation for correct answer:

Step 1: Estimate the sample space for three dices thrown at a time:

When three dice are thrown,

There are six independent options available for each dice.

So total number of sample spaces $=6^3$

Step 2: Estimate the set and thus the favourable cases:

Favorable cases are: $(4+6+6),(5+5+6),(5+6+5),(6+4+6),(6+6+4),(6+5+5)$

total favorable outcomes = $6$

Estimate the required probability:

P(getting $16$ in one throw with three dice is) will be as follows

$\begin{array}{rcl}P\left(A\right)& =& \frac{6}{216}\left[\text{∵p=}\frac{\mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}}\right]\\ & =& \frac{1}{36}\end{array}$

Hence, the probability of getting $16$ in one throw with three dice is $\frac{1}{36}$ .

Hence, option (A) is the correct answer.