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Chapter 4 Elementary Probability Theory
Chapter 4Elementary
Probability Theory
How Often Do Lie Detector’s Lie?
From Chances: Risks and Odds in Everyday Life by James Burke
If I take a polygraph test and lie, what is the risk that I will be detected?
What is the risk that if I take a polygraph test it will incorrectly say that I lied?
There is about a 72% chance of being caught in a lie by the machine.
Approximately 1 in 15 or 6.67% will be falsely accused of lying.
Conditional Probability
Determine the percentage of answers the polygraph will wrongly indicate as lies?
Determine the percentage of answers that the polygraph will correctly indicate as lies.
If the polygraph indicates that 30% of the questions were answered with a lie, what percentage of the time did the person actually lie?
Why would anybody study
PROBABILITY?
Chapter 4 ElementaryProbability
Theory
Section 1 What is
Probability?
Probability• Probability is a numerical measurement
of likelihood of an event.• The probability of any event is a number
between zero and one.• Events with probability close to one are
more likely to occur.• If an event has probability equal to one,
the event is certain to occur.
Probability Notation
If A represents an event, P(A)
represents the probability of A.
Three methods to find probabilities:
• Intuition
• Relative frequency
• Equally likely outcomes
Intuition method
based upon our level of confidence in the result
Example: I am 95% sure that I will attend school.
Probability as Relative Frequency
Probability of an event = the fraction of the time that the event
occurred in the past = fn
where f = frequency of an eventn = sample size
Example of Probability as Relative Frequency
If you note that 57 of the last 100 applicants for a job have been female, the
probability that the next applicant is female would be:
P Female( ) = 57100
Law of Large Numbers
In the long run, as the sample size increases and increases, the relative
frequencies of outcomes get closer and closer to the theoretical (or actual)
probability value.
Equally likely outcomes
No one result is expected to occur more frequently
than any other.
Probability of an event when outcomes are equally likely =
number of outcomes favorable to event
total number of outcomes
or
P Event( ) = frequency of successnumber of trials
Example of Equally Likely Outcome Method
When rolling a die, the probability of getting a number less than three =
P(<3) =
P(<3) =
2613
Statistical Experiment
An activity that results in a definite outcome
Sample Space
set of all possible outcomes of an experiment
Sample Space for the rolling of an ordinary die:
{1, 2, 3, 4, 5, 6}
For the experiment of rolling an ordinary die:
P(even number) =
P(even number) =
P(6) =
36
16
12
For the experiment of rolling an ordinary die:
P(~5) =
1 − 16
56
P(~5) =
P(~5) =
1 — P(5)
Complement of Event A
The event: not A~A
Probability of: not AP(~A)
Probability of: complement of AP(Ac)
The event: complement of AAc
Probability of a Complement
P(~ A) = P (Ac) = 1 – P(A)
Probability of a Complement
If the probability that it will snow today is 30%,
P(~snow)
1 – P(snow) 1 – 0.30
0.70
Probability Related to Statistics
• Probability makes statements about what will occur when samples are drawn from a known population.
• Statistics describes how samples are to be obtained and how inferences are to be made about unknown populations.
Probability Sample QuestionsWhat is the probability of selecting an ace from a deck of cards?
P Ace( )452113
Probability Sample QuestionsWhat is the probability of selecting a face card?
P Face Card( )1252313
Probability Sample Questions
What is the probability of not selecting a
face card?
P ~ Face Card( )
1− P Face Card( )1− 1252
4052
1013
P Ac( )
Homework Assignments
Pages 139 - 142Exercises : 1 - 21, oddExercises: 2 - 20, even
The End of
Section 1
