Question

An experiment consists of rolling three fair dice --- a red die, a blue die, and a white die --- and recording the number rolled on each die. Assume that the dice are fair, so that all outcomes are equally likely.
(1) What probability should be assigned to each outcome?
(2) What is the probability that the sum of the numbers rolled is 6?
(3) What is the probability that the sum of the numbers rolled is at most 5?

Answer 1

you have 6 possibilities for each die
by the counting principle the number of possibilities is therefore \(6\times 6\times 6=6^3\)
since each of these outcomes is presumed to be equally likely, they must all have the same probability, and those probabilities must add up to one, so they each have a probability of
\[\frac{1}{6^3}\]

Answer 2

the rest is counting
how many ways can you get a one on three dice, with the sophistication that for example \[(1,2,3)\] is a different roll than \((2,3,1)\)

Answer 3

rather how many ways can you get a 6 on three dice