1 / 52

Chapter 4

Chapter 4. Probability, Randomness, and Uncertainty. Section 4.1. Classical Probability. Vocabulary. Probability Experiment (trial) – any process in which the result is random in nature Outcome – each individual result that is possible

dara
Download Presentation

Chapter 4

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 4 Probability, Randomness, and Uncertainty

  2. Section 4.1 Classical Probability

  3. Vocabulary • Probability Experiment (trial) – any process in which the result is random in nature • Outcome – each individual result that is possible • Sample Space – the set of all possible outcomes for a given probability experiment • Event – a subset of outcomes of the sample space

  4. Tree Diagram

  5. Types of Probability • Subjective • An educated guess regarding the chance that an event will happen • Empirical • Experimental, probability of whatever happens in the experiment • Classical • Theoretical, probability of what is supposed to happen

  6. Empirical

  7. Classical Law of Large Numbers – the larger the number of trials, the closer the empirical probability will be to the true probability (classical)

  8. NOTE: Watch for problems with the words “at least” and “at most”

  9. Section 4.2a Probability Rules: Properties, the Complement, and Addition Rules

  10. Facts about Probability • Each outcome in the event has a probability between 0 and 1, inclusive. • The probability that an event is certain is 1. • The probability that an event will not happen is 0

  11. The Complement • The probability of the complement is all outcomes in the sample space that is not in E. • Example: • What is the complement of rolling an odd number? • Solution: An even number. (2, 4, 6)

  12. Complement

  13. Addition Rule • The probability of event E or event F happening is the probability of event E plus the probability of event F minus the probability of event E and event F. • The probability of event E and event F is what the two events have in common.

  14. Mutually Exclusive • Events that cannot happen at the same time. They do not have anything in common.

  15. To find the number of outcomes in an event that has 2 outcomes, raise 2 to the number of times you are “picking” In this case, it is .

  16. Section 4.2b Independence, Multiplication Rules, and Conditional Probability

  17. Multiplication Rules • “and” problems • With repetition • With replacement • Without repetition without replacement • Independent – one event has no effect on the other • Dependent – one event does have an effect on the other

  18. Independent Events If two events are independent, we multiply the probabilities of each event.

  19. Conditional Probability • The probability that an event happens given that something else happened first. • Example:

  20. Dependent Events The probability that event E and event F happening is equal to the probability of event E multiplied by the probability of event F happening given that event E happened first. The second probability is the conditional.

  21. Section 4.3 Counting Rules

  22. Fundamental Counting Principle • States that you can multiply together the number of possible outcomes for each stage in an experiment in order to obtain the total number of outcomes for that experiment.

  23. Special Combinations and Permutations

  24. Section 4.4 Additional Counting Techniques

More Related