1 / 5

3.1 Basic Concepts of Probability and Counting

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. 3.1 Basic Concepts of Probability and Counting.

nuncio
Download Presentation

3.1 Basic Concepts of Probability and Counting

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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. 139 (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. 135 for information on determining the likelihood of an event. • Practice: • #42 p. 140 • #46 p. 140 (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. 134) • Subjective Probability • Based on intuition or an educated guess. • Practice: • #56 p. 141 • Historical Note: Joseph Jagger (1875 Monte Carlo Casino)

More Related