# 9.1 Understanding Probability

```9.1 Understanding Probability
Remember to Silence Your
Cell Phone and Put It In
Defining Probability
The use of numbers to describe the
chance that something will happen.
The ratio of favorable occurrences to
the number of total possible
occurrences of an observable event.
For this class, unless asked to do differently,
fractions
Terminology
Experiment
Outcome
Sample Space
Equally Likely
Uniform Sample Space
Nonuniform Sample Space
Event
Example
Uniform Sample Space
Example
Nonuniform Sample Space
Defining Probability (cont.)
Probability, P, of an event A for a
uniform sample space:
P( A ) 
Number of outcomes associated with the event A
Number of outcomes in the sample space S
Probability, P, of an event A for a
nonuniform sample space:
P( A ) 
Measure of the outcomes associated with the event A
Measure of all of the outcomes in the sample space S
Terminology (cont.)
Random Event
Certain Event
Impossible Event
Complementary Events
Mutually Exclusive Events
Non-mutually Exclusive Events
Properties of Probability
1. 0  P(A)  1
2. The sum of the probabilities of all
outcomes in the sample space is 1
3. P(a certain event) = 1
4. P(an impossible event) = 0
5. If A and B are complementary events,
P(A) = 1 – P(B)
Properties of Probability (cont.)
6. If A and B are mutually exclusive
events, P(A or B) = P(A) + P(B)
7. If A and B are non-mutually exclusive
events, P(A or B) = P(A) + P(B) – P(A
and B)
Law of Large Numbers
Empirical Probability
Theoretical Probability
Law of Large Numbers

If an experiment is repeated many times,
the empirical probability of an event will
approach the theoretical probability of the
event occurring.
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