1 / 11

Chapter 6 - Probability

Chapter 6 - Probability. Math 22 Introductory Statistics. Simulating Repeated Coin Tosses. Simulation with the TI – 83 Empirical Probability (Observed Probability) – The probability of a specific event as it was observed in an experiment.

delano
Download Presentation

Chapter 6 - Probability

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. Chapter 6 - Probability Math 22 Introductory Statistics

  2. Simulating Repeated Coin Tosses • Simulation with the TI – 83 • Empirical Probability (Observed Probability) – The probability of a specific event as it was observed in an experiment. • Theoretical Probability – The true probability of a specific event of interest. Often an unknown value estimated by an empirical probability.

  3. Probability • Probability - A numerical value that is associated with some outcome and indicates how likely it is that the outcome will occur. • Experiment - The process of making an observation or taking a measurement. • Sample Space (S) - Listing of all possible outcome of an experiment. • Event - Subset of the sample space.

  4. Probability of an Event The probability of an event A is the sum of the outcomes in A. We write it as P(A). P(event) = # of times that the event can occur total # of outcomes in the experiment

  5. Assigning Probabilities to Individual Outcomes In assigning probabilities to the individual outcomes in a sample space, two conditions must be satisfied: • The probability of each outcome must be between 0 and 1, inclusive. • The probabilities of all outcomes in the sample space must sum to 1.

  6. Calculating the Probability of an Event • Define the experiment and list the outcomes in the sample space. • Assign probabilities to the outcomes such that each is between 0 and 1. • List the outcomes of the event of concern. • Sum the probabilities of the outcomes that are in the event of concern.

  7. Law of Large Numbers • As the number of times an experiment is repeated increases (as n gets larger), the value of the empirical probability will approach the value of the theoretical probability.

  8. Odds and Compliment of an Event • Odds • Compliment of an Event – The probability of that event nothappening.

  9. General Addition Rule • Let A and B be events then,

  10. Conditional Probability • Conditional Probability - The probability of an event occurring given that another event has already occurred.

  11. The Multiplication Law for Independent Events • Let A and B be two independent events then P(A and B)=P(A)P(B)

More Related