3.1 Basic Concepts of Probability and Counting
• What are we going to learn about?
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Probability Experiments
The Fundamental Counting Principal
The Three Different Types of Probabilities
Complementary Events
Applications
3.1 Basic Concepts of Probability and Counting
• What exactly is a probability experiment?
– Any chance process whose results can be well defined.
• Examples: Card Draw, Coin Toss, Lottery Pick, etc.
– Terms to know:
• Outcome = the result of a single trial of an experiment.
• Sample Space = the set of all possible outcomes in an experiment.
The sample space is usually denoted by S.
• Event = a subset of the sample space.
Events are usually denoted by capital letters A, B, C, etc.
*Remember that sample spaces and events are both sets!
– Practice:
• #22 p. 141 (sort of)
• Rolling the dice
3.1 Basic Concepts of Probability and Counting
• How do we calculate the probability of an event?
– Classical (or Theoretical) Probability
• The theoretical probability of event E is the ratio of the
number of outcomes in E to the total number of outcomes in
the sample space S.
PE 
nE
Number of outcomes in event E

Total number of outcomes in the sample space S n  S 
• Assumes all outcomes are equally likely.
3.1 Basic Concepts of Probability and Counting
• Properties of Probabilities
– The probability of any event E will always be between 0
and 1 inclusive.
– The probability of an event that cannot occur is 0.
– The probability of an event that is certain to occur is 1.
– See p. 137 for information on determining the likelihood
of an event.
– Practice:
• #52 p. 142
• #56 p. 143 (complementary events)
3.1 Basic Concepts of Probability and Counting
• Other Types of Probability
– Empirical (or Statistical) Probability
• Based on collected observations
• Represents the relative frequency of an event.
• As the number of repetitions of an experiment increases,
Empirical Probability of E → Theoretical Probability of E
(Law of Large Numbers p. 136)
– Subjective Probability
• Based on intuition or an educated guess.
– Practice:
• #38 p. 142
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Historical Note: Joseph Jagger (1875 Monte Carlo Casino)