Question

If three dice are throw simultaneously, then the probability of getting a score of 5 is
(a) 5/216
(b) 1/6
(c) 1/36
(d) none of these

Answer 1

(c) 1/36

When three dice are thrown together, the sample space S associated with the random experiment is given by
S = {(1, 1, 1), (1, 1, 2), (1, 1, 3) ...(6, 6, 5), (6, 6, 6)}
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)}
∴ Favourable number of elementary events = 6
i.e. n(A) = 6
Hence, required probability = $\frac{6}{216}=\frac{1}{36}$