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3.1 Basic Concepts of Probability and Counting

Learn about probability experiments, the fundamental counting principal, different types of probabilities, complementary events, and applications, including classical and empirical probability. Understand properties of probabilities and other types like subjective probability. Explore examples like card draw, coin toss, and lottery pick to grasp key concepts efficiently.

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3.1 Basic Concepts of Probability and Counting

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  1. 3.1 Basic Concepts of Probability and Counting • What are we going to learn about? • Probability Experiments • The Fundamental Counting Principal • The Three Different Types of Probabilities • Complementary Events • Applications

  2. 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. 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. • Assumes all outcomes are equally likely.

  4. 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)

  5. 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 • Historical Note: Joseph Jagger (1875 Monte Carlo Casino)

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