Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 14- 1

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 14 From Randomness to Probability

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Dealing with Random Phenomena A random phenomenon is a situation in which we know what outcomes could happen, but we don’t know which particular outcome did or will happen.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Dealing with Random Phenomena Pop Quiz 1. Who is George W. Bush's favorite Friend? a. Chandler b. Joey c. Monica d. Pheobe e. Rachael f. Ross

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Dealing with Random Phenomena 2. How many cousins does Professor DeMaio have? a. 1 b. 2 c. 3 d. 4 e. 5

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Dealing with Random Phenomena For both questions random guessing must be employed. The probability of a correct answer in question number 1 is 1/6 or about 16.67%. The probability of a correct answer in question number 2 is 1/5 or 20%. This concept of counting and dividing is the heart of computing probabilities.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Probability The probability of an event is its long-run relative frequency. While we may not be able to predict a particular individual outcome, we can talk about what will happen in the long run. For any random phenomenon, each attempt, or trial, generates an outcome. Something happens on each trial, and we call whatever happens the outcome. These outcomes are individual possibilities, like the number we see on top when we roll a die.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Probability (cont.) Sometimes we are interested in a combination of outcomes (e.g., a die is rolled and comes up even). A combination of outcomes is called an event. An experiment consists of randomly picking a card from a standard deck of playing cards (no jokers). Some possible outcomes of this experiment are listed below. A - The 8 of clubs is selected. B - A red card is selected. C - The Jack of hearts is not selected.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Probability (cont.) An experiment consists of watching ten different movies made after 1982 and recording if a Coke product appears in the film. List some possible outcomes of this experiment.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Probability (cont.) When thinking about what happens with combinations of outcomes, things are simplified if the individual trials are independent. Roughly speaking, this means that the outcome of one trial doesn’t influence or change the outcome of another. For example, coin flips are independent.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Probability (cont.) Two events A and B are disjoint or mutually exclusive if they cannot occur at the same time. example: Let an experiment consist of rolling a pair of fair dice. Consider the following events. A - The sum of the two dice is an even number. B - The sum of the two dice is an odd number. C - The sum of the two dice is 7. Are events A and B mutually exclusive? Explain. Are events A and C mutually exclusive? Explain. Are events B and C mutually exclusive? Explain.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Law of Large Numbers The Law of Large Numbers (LLN) says that the long-run relative frequency of repeated independent events gets closer and closer to the true relative frequency as the number of trials increases. For example, consider flipping a fair coin many, many times. The overall percentage of heads should settle down to about 50% as the number of outcomes increases.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Law of Large Numbers (cont.) The common (mis)understanding of the LLN is that random phenomena are supposed to compensate some for whatever happened in the past. This is just not true. For example, when flipping a fair coin, if heads comes up on each of the first 10 flips, what do you think the chance is that tails will come up on the next flip?