on and for problems 10 and 11, that we have a simple definition for the probability
of an event occurring. Let S be the sample space, that is, the set of all possible outcomes of
an experiment (such as rolling dice, or drawing cards, etc.). An event E is a specified set
of outcomes, that is, $E \subset S$. Then, the probability that the event E occurs is, $prob(E) = \frac{|E|}{|S|}$, that is the number of outcomes in E divided by the total number of possible
outcomes. As an example, if one rolls one die, then $S = \{1, 2, 3, 4, 5, 6\}$ is the set of all
possible rolls of the one die. Suppose we want to know the probability that the roll is even.
Here, $E = \{2, 4, 6\}$. The probability that the roll is even is $prob(roll \text{ is even}) = prob(E) = \frac{|E|}{|S|} = \frac{3}{6} = \frac{1}{2}$.
Suppose you have three standard (six-sided) dice. (Think of them as having three colors,
so you can keep track of which is which.)
(a) How many different rolls of the three dice are there?
(b) How many ways are there to roll the dice so they sum to 17? What is the probability
that the sum if a given roll is 17?
(c) How many ways are there to roll 16? What is the probability that the roll is 16?
