Transcript Anatomy: Probability, Basic Terms

ANATOMY OF BASIC PROBABILITY
PROBABILITY is a measure of how likely an outcome or event is.
THE RULES
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The probability of the occurrence of an event is always between 0 and 1.
The probability of an impossible event is equal to 0.
The probability of an event that is certain to occur is equal to 1.
In a probability distribution the sum of the probabilities = 1.
THE TERMINOLOGY
THE NOTATION
EXPERIMENT - In statistics, the word “experiment” is used in a very wide,
and unconventional, sense. In probability an experiment refers to a process for
which the outcome is unknown until the experiment has concluded. For
example, the rolling of a fair die is an experiment with an unknown outcome.
In probability, events are usually denoted by uppercase letters (A, B, C, etc.).
Using notation, “the probability of A” is written like this: P(A).
“The complement of A” is written like this: P(A).
OUTCOMES - are the results one obtains from an experiment (e.g. rolling a
2) is one possible outcome when tossing a fair die.
THE EXPERIMENT
SAMPLE SPACE - is the set of all possible outcomes of any experiment. For
example, the sample space for the rolling of a fair die is {1, 2, 3, 4, 5, 6}. The
sample space is often denoted s. Using the above example, s = {1, 2, 3, 4, 5, 6}
Suppose we roll a fair die one time. The sample space for this experiment is
s = {1, 2, 3, 4, 5, 6}. Now let’s say that our event of interest is rolling a 4. We
will call it “Event A.” then:
EVENT - An event is a subset of the sample space. Rolling a 5 on the toss of a
fair die is an event. It is a subset of the sample space defined above.
P ( A) 
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and “the complement of event A” will be denoted like this:
COMPOUND EVENT – occurs when more than one SIMPLE EVENT is
possible. Obtaining a 5 on the roll a pair of dice is a compound event as there
are several ways the outcome could be 5 (s = {(1, 4), (2, 3), (3, 2), (4, 1)}. Note
that within this compound event there are four simple events.
COMPLEMENTARY EVENT - is the nonoccurrence of an event in the
sample space. For example rolling a 5, is an event. Not rolling a 5 is the
complement of that event.
P( A) 
IMPORTANT STUFF:
Take special note of the fact that the sum of an event and its
complement is equal to 1. This will always be the case, no matter
what the experiment or event of interest.
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