Question

If three dice are throw simultaneously, then the probability of getting a score of 5 is

• A. $\frac{5}{216}$
• B. $\frac{1}{6}$
• C. $\frac{1}{36}$
• D. none of these

Answer 1

The correct option is C

$\frac{1}{36}$

When three dice are thrown together, the sample space S associated with the randsom experiment is given by

$S=\left\{\right(1,1,1),(1,1,2),(1,1,3),.......(6,6,5),(6,6,6\left)\right\}$

Clearly, total number of elementary events n(S) = 216

Let A be the event of getting a total score of 5

Then A = {(1, 1, 3), (1, 3, 1), (3, 1, 1), (1, 2, 2),(2, 1, 2), (2, 2, 1)}

$\therefore$ Favourite number of elementary events = 6

i.e., n(A) = 6

Hence, required probability $=\frac{6}{216}$

$=\frac{1}{36}$