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Lecture

# Notation, basic rules of probability, conditional probabilities

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Department
Statistics
Course
STAT 301
Professor
Brett Hunter
Semester
Fall

Description
29 August Probability is the likelihood of occurrence of some outcome or event An experiment is a process that leads to only one outcome out of several possibilities An outcome is a particular result of an experiment An event is a collection of one or more outcomes Denote by capital letter (A, B, C) The sample space is all possible outcomes of an experiment Denoted by Ω (this is capital omega) C The complement of A, denoted A , are all outcomes in Ω which are not A. Example A fair coin is tossed twice What is the sample space? Ω = {HH, HT, TH, TT} What is the probability of getting 2 heads? ¼ What is the probability of getting at least one tails? ¾ We say two events are mutually exclusive if both can’t occur at the same time. We also call these disjoin events. E.g. Event A: Roll a 3 Event B: Roll an even # If I roll only 1 die, only one of A and B can occur, so A and B are disjoint. We say events are collectively exhaustive if at least one of the events must occur when the experiment is conducted. Notation P(A) is the probability that event A occurs. P(A and B) = P(A ∩ B) ∩ - intersect Probability that both events A and B occur Known as the “intersection of A and B” P(A or B) = P(
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