Basic Probability Chapter Goal: Explain basic probability concepts and definitions Use contingency tables to view a sample space Apply common rules of probability Compute conditional probabilities Determine whether events are statistically independent

Definitions: Probability – the chance or likelihood that an uncertain (particular) event will occur Probability is always between 0 and 1, inclusive There are three approaches to assessing the probability of un uncertain event: 1. a priori classical probability– based of a prior knowledge 2. empirical classical probability– based on observed data 3. subjective probability -- an individual judgment or opinion about the probability of occurrence

Basic Concepts: Sample Space – the collection of all possible events An Event – Each possible type of occurrence or outcome from the sample space Simple Event – an event that can be described by a single characteristic Complement of an event A -- All outcomes that are not part of event A Joint event --Involves events that can be described by two or more characteristics simultaneously

Basic Concepts: Continued Mutually exclusive events: Events that cannot occur together Collectively exhaustive events One of the events must occur The set of events covers the entire sample space The probability of any event must be between 0 and 1, inclusively. That is: 0 ≤ P(A) ≤ 1 for any event A The sum of the probabilities of all mutually exclusive and collectively exhaustive events is 1 exhaustive. That is, if A, B, and C are mutually exclusive and collectively exhaustive event, then (the entire sample space)

Contingency Tables: A sample space can be presented by a contingent table (C.T.) It is very useful for the study of empirical probabilities Example: Let’s say 400 managers were surveyed about booking airline tickets and researching prices of tickets in the internet Sample Space: Total Number of Managers Surveyed   Booked Airline Ticket in the Internet Yes, B1 No, B2 Totals Researched Prices in the Internet Yes, A1 88 124 212 No, A2 20 168 188 108 292 400

Computing Simple (Marginal) Probobilities. Where B1, B2, …, Bk are k mutually exclusive and collectively exhaustive events Probability of a joint event, A and B: How many simple events are in my example? How many joint events are in my example?

Rules of Probability: General Addition Rule P(A or B) = P(A) + P(B) - P(A and B) If A and B are mutually exclusive, then P(A and B) = 0, so the rule can be simplified P(A or B) = P(A) + P(B) If A and B are collectively exhaustive, then P(A or B) = P(A) + P(B)=1

A conditional probability is the probability of one event, given that another event has occurred: The conditional probability of A given that B has occurred The conditional probability of B given that A has occurred Where P(A and B) = joint probability of A and B P(A) = marginal probability of A P(B) = marginal probability of B

Multiplication Rule– for two events A and B Two events A and B are statistically independent if the probability of one event is unchanged by the knowledge that other even occurred. That is: Then the multiplication rule for two statistically independent events is: