Chapter 4 Flashcards
Probability
Numerical value that measures the likelihood that an event occurs
Experiment
Process that leads to one of several possible outcomes
Sample Space
A record of all possible outcomes of an experiment
Event
Subset of a sample space
Exhaustive Event
When all possible outcomes of an experiment are included in the events
Mutually Exclusive Event
When events have no common outcomes of an experiment
Union
The union of two events consisting of outcomes in A or B
Denoted as: A U B
Intersection
Intersection of two events consisting of outcomes in A and B
Denoted as: A n B
Complement
Consists of all outcomes in sample space S not in A
Denoted as: A(super(c))
Subjective Probability
Probability value based on personal and subjective judgement
Empirical Probability
Probability based on observing the relative frequency with which an event occurs
Classical Probability
Probability used in games of chance.
Based on assumption that all outcomes are equally likely
Law of Large Numbers
If an experiment is repeated a large number of times, its empirical probability approaches its classical probability
Complement Rule
Probability of the complement of event A:
P(A(super c)) = 1 - P(A)
Addition Rule
Probability that A or B occurs:
P(A U B) = P(A) + P(B) - P(A n B)
Joint Probabilitiy
Values in the interior of a joint probability table, representing the probabilities of the intersection of two events
Conditional Probability
Probability of an event given that another event has already occurred
Unconditional Probability
Probability of an event without any restriction
Unconditional Probability
Probability of an event without any restrictions
Conditional Probability Formula
P(A|B) = P(A n B) / P(B)
Independent
Occurrence of one event does not affect the probability of the occurrence of the other event
Dependent
Occurrence of one event is related to the probability of the occurrence of the other
Total Probability Rule
Expresses the unconditional probability of an event, P(A), in terms of probabilities conditional on various mutually exclusive and exhaustive events
Bayes’ Theorem
Rule for updating probabilities is
P(B|A) = P(A|B)P(B)/P(A|B)P(B) + P(A|Bc) * P(Bc)
where P(B) is the prior probability and P(B|A) is the posterior probability
Prior Probability
Unconditional probability before the arrival of new information
