
Identify the experiment. What, exactly, is being done.

Identify the Sample Space S. Write out a few outcomes of the experiment (as in problems [1] to [10] below)

Noting how S is built, count the size of S using the appropriate tool,
that is, how many different outcomes does the experiment have (as in [3], [6], [8], and [10] below)?

Identify the event E. Write down a few outcomes in E (as in [2], [5], [7], and [9] below)

Noting how E is built, count the size of E using the appropriate tool,
that is, in how many different ways can E occur (as in [3], [6], [8], and [10] below)?

The probability of E is then [ the size of E ] divided by [ the size of S ], that is,
the probability of E is then
[ the number of ways the event can occur ] divided by [ the number of ways the experiment can end ],

An example of the above procedure (similar to examples done in class):
Question: What is the probability that a 5card poker hand contains exactly 2 aces?
The experiment: Draw 5 cards (that is, a quintuple) from a 52card deck
The sample space S: the set of quintuples, such as { K♠, K♣, 4♥, J♥, 3♦ }.
The size of S: C(52,5) since a poker hand is an unordered 5card subset of the deck
The event E: the set of quintuples which include exactly 2 aces, such as { Q♠, A♣, A♥, 2♦, 3♦ }
The size of E: C(4,2) aces, C(48,3) nonaces, so size of E is the product C(4,2)C(48,3) using multiplication rule
The probability of E: [C(4,2)C(48,3)] divided by C(52.5), which is about 0.04
