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Section 5.1 –Probability Rules
Probability
– a measure of the likelihood of a random phenomenon or chance behavior.
Probability deals with experiments that yield shortterm results (outcomes) and reveal longterm
predictability.
The longterm proportion with which a certain outcome is observed is the
probability
of that outcome.
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.
Sample Space
– The collection of all
possible outcomes.
Denoted S.
Event
– A collection of outcomes from a probability experiment. (may consist of one or more outcomes)
Events are usually denoted with capital letters.
P(E)
means the “probability that event E occurs”
Probability Rules
:
1.
For any event E,
____ ≤
P(E)
≤ ____ .
2.
An impossible event has probability ________.
3.
An event certain to occur has probability ________.
4.
The sum of the probabilities of all outcomes must equal _____.
5.
An event with a probability less than 0.05 (5%) is considered
_________________
.
Different Ways to Compute Probability
:
1.
Approximating Probabilities using the Empirical Approach
:
Perform a procedure a large number of times and record how many times event A occurs.
P(E) =
eriment
the
in
trials
of
number
occurs
E
times
of
number
exp
Example
:
During his career, Reggie Miller made 5915 of 6679 free throw attempts after being fouled.
Find the probability that Reggie Miller will make a free throw after being fouled.
Example
:
In a movie theater, 50 people have popcorn and 35 people do not.
What is the probability that
a randomly selected person has popcorn?
1
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probability model
lists all possible outcomes of a probability experiment along with each outcome’s
probability.
Example
:
Build a probability model for cola preference in your class.
Would it be unusual to randomly select an individual who likes Pepsi?
2.
Computing Probabilities Using the Classical Method
:
Each simple event must have an equal chance of occurring (ie, outcomes must be
equally likely
)
P(E) =
outcomes
possible
of
number
occur
can
E
ways
of
number
Example
:
A multiple choice test has 5 choices for each problem.
What is the probability that if you
guess, you will guess incorrectly?
Example
:
Roll 2 dice.
What is the probability of getting a sum of 9?
What is the probability of getting a sum of 7?
Favorite Cola
Frequency
Probability
Coke
Pepsi
Dr. Pepper
1
2
3
4
5
6
1
2
3
4
5
6
7
2
3
4
5
6
7
8
3
4
5
6
7
8
9
4
5
6
7
8
9
10
5
6
7
8
9
10
11
6
7
8
9
10
11
12
2
Example
:
If a person is randomly selected, find the probability that his or her birthday is September 26
th
.
Find the probability that his or her birthday is in December.
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This note was uploaded on 01/06/2012 for the course MATH 1342 taught by Professor Lisajuliano during the Spring '12 term at Collins.
 Spring '12
 LisaJuliano
 Probability

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