Introduction to probability

Mathematics of “random experiments”

1 - Set 2 - Probability

The set contains all possible outcomes of the experiments. Called “Sample space”. Denoted by “S”

The subsets of a set are called events. • If A is an event, then A is a subset of S • If A is an event, A° = S - A –> A° is a complement of A

• A∩B = {s ϵ S: s ϵ A, s ϵ B} • AUB = {s ϵ S: s ϵ A or s ϵ B}

A probability is a way of assigning to each event A a number P(A) (probability of A) in such a way the following properties are satisfied: a) 0<P(A)<1 and P(S) = 1 b) If A and B are disjoint events that: - A∩B=0 - P(AUB) = P(A) + P(B)

1 - -> A and B are two events -> A is a subset of B -> B-A = {s ϵ B, s !ϵ A} -> If B = S then P(A°) = 1 - P(A) -> A and B-A are disjoint and A U (B-A) = B so by additivity P(B) = P(A) + P(B-A) 2 - P(AUB)=P(A)+P(B)-P(A∩B)