1 / 31

Y. Davis Geometry Notes

This chapter provides an overview of probability and combinations, including the fundamental counting principle, permutations, combinations, geometric probability, simulation, random variables, and more. Learn how to calculate probabilities and understand the concepts with clear explanations and examples.

chenoweth
Download Presentation

Y. Davis Geometry Notes

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. Y. Davis Geometry Notes Chapter 13

  2. Probability Favorable outcome Possible outcome

  3. Sample space A set of all possible outcomes of an experiment.

  4. Tree Diagram

  5. Experiments Two stage experiments—an experiments with 2 stages or events. Multi-stage experiments—an experiment with more than 2 stages or events.

  6. Fundamental Counting Principle The number of outcomes in a sample space can be found by multiplying the number of possible outcomes.

  7. Permutation An arrangement of objects in which order is important.

  8. Factorial n! Of a positive integer n is the product of the positive integers less than or equal to n.

  9. Permutations The number of permutations of n distinct objects taken r at a time is denoted by

  10. Permutations with repetition The number of distinguishable permutations of n objects in which one object is repeated r1 times, and another is repeated r2 times, and so on, is

  11. Circular Permutations Objects are arranged in a circle or loop. The number of distinguishable permutations of n objects arranged in a circle with no fixed reference points is

  12. Combination An arrangement of objects in which order is not important.

  13. Combinations The number of combinations of n distinct objects taken r at a time is denoted by

  14. Geometric Probability Probability that involves geometric measures such as length or area .

  15. Length Probability Ratio

  16. Area Probability Ratio

  17. Probability Model A mathematical model used to match a random phenomenon.

  18. Simulation The use of a probability model to recreate a situation again and again so that the likelihood of various outcomes can be estimated.

  19. Random Variable Is a variable that can assume a set of values, each with a fixed probabilities.

  20. Expected value Also known as mathematical expectation, is the average value of a random variable that one expects after repeating an experiment or simulation a theoretically infinite number of times.

  21. Law of Large numbers As the number of trials of a random process increases, the average value will approach the expected value.

  22. Compound Event Consist of 2 or more simple events.

  23. Independent Events The probability that one event occurs does not affect the probability that the 2nd event occurs.

  24. Dependent Events The probability that one event occurs in some way changes the probability that the 2nd event occurs.

  25. Probability of 2 independent events P (A and B) = P(A)·P(B)

  26. Probability of 2 dependent events P(A and B)=P(A)·P(B|A) P(B|A) read probability that event B occurs given that event A has already occurred. This is known as conditional probability.

  27. The conditional probability of B given A isP(B|A)= , where P(A)≠0

  28. Mutually exclusive When 2 events cannot happen at he same time. The 2 events have no outcome in common.

  29. Probability of Mutually Exclusive Events P(A or B)=P(A)+P(B)

  30. Probability of non-mutually exclusive events P(A or B)=P(A)+P(B)-P(A and B)

  31. Complement Consist of all the outcomes in a sample space that are not included as outcomes of the event. P(not A)=1-P(A)

More Related