Three fair six-sided dice are thrown, and the score is the sum of the three results. What is the probability that the score is less than $6$?
closed as off-topic by Namaste, Matthew Conroy, JMoravitz, TravisJ, N. F. Taussig May 1 '17 at 20:01
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Let $P(X<6)$, where $X =$ the sum of $x_1, x_2, x_3 $
In this case, we can simply list out all the outcome such $P(X<6)$
- $(1,1,1), (1,1,2), \dots, (1,1,3), \dots, (3,1,1).$
Note that each event has the same probability:
- Find the probability of one event: $P(x_1 \cap x_2 \cap x_3) $
Connecting both 1. and 2. you should be able to go on to the next and final step to solving the problem.