Possible Outcomes and Sums
Just as one die has six outcomes and two dice have 62 = 36 outcomes, the probability experiment of rolling three dice has 63 = 216 outcomes. This idea generalizes further for more dice. If we roll n dice then there are 6n outcomes.
When all three dice are rolled at the same time what is the probability of rolling the same number on all dice?
Multiplying this together gives 163 for the probability that all dice are a 1. We have the same chance (163) of rolling three 2s, three 3s, three 4s, three 5s, or three 6s, so the probability of rolling any number on all three dice at the same time is 6⋅163, or 136.
What is the sample space when three dice are rolled?
When three dice are rolled sample space contains 6 × 6 × 6 = 216 events in form of triplet (a, b, c), where a, b, c each can take values from 1 to 6 independently. Therefore, the number of samples is 216.
