Statistics
A First Course
Donald H. Sanders
Robert K. Smidt
Aminmohamed Adatia
Glenn A. Larson
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Chapter 4
Probability Concepts
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Chapter 4 - Topics
• Some Basic Considerations
• Probabilities for Compound Events
• Random Variables, Probability Distributions,
and Expected Values
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Some Basic Considerations
• Probability Experiment
– Any action for which an outcome, response, or
measurement if obtained that can’t be predicted
with certainty
• Event
– Subset or collection of outcomes from the
sample space
• Simple Event
– An event that can’t be broken down any further
• Sample Space
– Set of all possible simple outcomes, responses,
or measurement of an experiment
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Some Basic Considerations
• Probability
– Relative likelihood of that event occurring
Classical (a priori) Probability
Relative Frequency (Empirical) Probability
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Probabilities for Compound Events
• Compound Event
– Combination of two or more events
• Conditional Probability
– Probability that one event will occur given
that another event has already occurred
• Joint Probability
– Probability that two or more events occur
such that the second event occurs after the
first event
• Events could be dependent or independent
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A tree diagram showing all the
possible outcomes of drawing 2
pieces from 5 red, 3 green, and 2
yellow candies. Note that the total
probability is 90/90 or 1.
Figure 4.5
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Probabilities for Compound Events
• Dependent Events
– The occurrence of one event affects the
probability of the occurrence of another
event
Joint Probability: Multiplication Rule
where P(B|A) is the conditional probability of event B occurring
given that event A has occurred
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Probabilities for Compound Events
• Independent Events
– The occurrence of one event does not affect
the probability of the occurrence of another
event
Joint Probability: Multiplication Rule
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Probabilities for Compound Events
• Mutually Exclusive Events
– Events cannot occur at the same time
Venn Diagram
Addition Rule
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Probabilities for Compound Events
• Non-mutually Exclusive Events
– Events can occur at the same time
Venn Diagram
Addition Rule
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Probabilities for Compound Events
• Complement of an Event
– Consists of all possible outcomes from the
sample space that are not in event
Rule for Complementary Events
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Random Variables, Probability
Distributions, and Expected Values
• Random Variable
– Single numerical value for each outcome of a
probability experiment
• Discrete Random Variable
– All possible values can be counted or listed
• Continuous Random Variable
– Infinite number of values that can fall, without
interruption, along an unbroken interval
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Random Variables, Probability
Distributions, and Expected Values
• Probability Distribution
– Discrete random variable
– Gives probability for each of the values of
the random variable
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Distribution of the sum of the
numbers thrown on one toss of
two fair dice
Figure 4.6
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A histogram of the probability
distribution of the results of throwing
a pair of dice.
Figure 4.6
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Random Variables, Probability
Distributions, and Expected Values
Expected Values: Mean of Random Variable Formula
Standard Deviation of Random Variable Formula
Method 1
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Shortcut Method
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End of Chapter 4
Probability Concepts
© 2005 McGraw-Hill Ryerson Ltd.
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