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# PROBABILITY BASICS

## by Wilkes University on Feb 24, 2011

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• seahag49 Very good introduction to probability basics. 11 months ago
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## PROBABILITY BASICSPresentation Transcript

• Probability is a measure of the likelihood of a random phenomenon or chance behavior.
Probability describes the long-term proportion with which a certain outcome will occur in situations with short-term uncertainty.
• The Law of Large Numbers
As the number of repetitions of a probability experiment increases, the proportion with which a certain outcome is observed gets closer to the probability of the outcome.
• …Some Definitions…
An experiment is any process that can be repeated in which the results are uncertain.
A outcome is the result of an experiment.
The sample space of a probability experiment is the collection of all possible outcomes.
• …Some Definitions…
An event is a collection of outcomes from a probability experiment.
A simple event is one of the possible outcomes…
A joint event is more than one of the possible outcomes…
• …More Definitions…
Mutually exclusive events vs. Collectively exhaustive events

at least one of the events must occur
cannot occur at the same time (i.e., they have no common outcomes).
Independent events vs. Dependent events
• Three methods for determining the probability of an event:
the classical method
The classical method of computing probabilities requires equally likely outcomes.
An experiment is said to have equally likely outcomes when each simple event has the same probability of occurring.
• Computing Probability Using the Classical Method
If an experiment has equally likely simple events, then the probability of E, P(E), is
…need prior information on E…
• Three methods for determining the probability of an event:
(1) the classical method
(2) the empirical method
(relative frequency)
• Computing Probability Using the Empirical Method
The probability of an event E is approximately the number of times event E is observed divided by the number of repetitions of the experiment.
…need data frequencies from an ‘experiment’ …
• Three methods for determining the probability of an event:
(1) the classical method
(2) the empirical method
(3) the subjective method
• Subjective probabilities are probabilities obtained based upon an educated guess.
• Properties of Probabilities
The probability of any event E, P(E), must be between 0 and 1 inclusive.
If an event is impossible, the probability of the event is 0.
If an event is a certainty, the probability of the event is 1.
The sum of the probabilities across all possible outcomes of an experiment is equal to 1.
S = {e1, e2, …, en}, then P(e1) + P(e2) + … + P(en) = 1.
• …Probability Rules…
E
• …Probability Rules…
E
• E
F
…Probability Rules…
Let E and F be two events…
{EandF} is the event consisting of simple events that belong to both E and F.
{EorF} is the event consisting of simple events that belong to either E or F but not both.
For any two events E and F…
P(E or F) = P(E) + P(F) – P(E and F)
…Probability Rules…
OR probabilities
E
F
• …Probability Rules…
E
F
Addition Rule for Mutually Exclusive Events
If E and F are mutually exclusive events, then…
P(E or F) = P(E) + P(F)
cannot occur at the same time (i.e., they have no common outcomes).
• …Probability Rules…
Conditional Probability, P(F|E)
The notation P(F | E) is read “the probability of event F given event E”.
It is the probability of an event F given the occurrence of the event E.
• …Probability Rules…
• …Probability Rules…
Two events E and F are independent if the occurrence of event E in a probability experiment does not affect the probability of event F.
Two events are dependent if the occurrence of event E in a probability experiment affects the probability of event F.
• …Probability Rules…
• …Probability Rules…