Question

Three dice are thrown simultaneously. What is the probability of getting 15 as the sum?

 

Answer 1

If three dices are thrown simultaneously, then the number of all the possible outcomes are 6³ = 216.
∴ Total  number of possible outcome = n(S) = 216
Let A be the event of getting a sum of 15 when three dices are thrown simultaneously.
The favourable outcomes are as follows:
A = {(3,6 , 6), (4, 6, 5), (5, 6, 4), (6, 6, 3), (6, 3, 6), (6, 4, 5), (6, 5, 4), (4, 5, 6), (5, 5, 5), (5, 4, 6)}
i.e. number of favourable outcomes = n(A) = 10
Hence, required probability = P (getting a sum of 15) = \[\frac{10}{216}\]