Compliment: The compliment of an event A, is the set of all outcomes in S that are not in A
Mutually Exclusive Events: When and B have no common outcomes, they are said to be mutually exclusive or disjoint events, i.e. $P=(A \cap B) = 0$
Axiom:
1. For event A, P(A) >= 0
2. P(S) = 1
3. (Need to look at slides to correct)
(a) If $A_1, A_2 ... A_k$ is a finite collection of mutually exclusive events then: $$P(A_1 \cup A_2 \cup ... \cup A_k) = \sum^{\infty}_{i=1} P(A_i) $$
(b) If $A_1, A_2 ... A_k$ is a finite collection of mutually exclusive events then: $$P(A_1 \cup A_2 \cup ... \cup A_k) = \sum^{\infty}_{i=1} P(A_i) $$
Proposition:
1. For event A, P(A) = 1 - P(A')
2. If and and B are mutually exclusive then $P(A \cap B) = 0$
Permutation: Any ordered sequence of k objects taken from a set of n distinct objects is called a permutation of size k of the objects. The number of permutations of size k that can be constructed from n objects is denoted by $P_{k,n}$ and calculated by:
$$
P_{k,n} = \frac{n!}{(n-k)!}
$$
Combination: Given a set of n, any unordered sub-set of k of the objects is called a combination. The set of combinations of size k that can be formed from n distinct objected will be denoted by $C_{k,n}$ and calculated by:
$$
C_{k,n} = \frac{n!}{k!(n-k)!} = \begin{pmatrix}n \\ k \end{pmatrix}
