Probability complete - Stat 250 Gunderson Lecture Notes...

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33 Stat 250 Gunderson Lecture Notes Chapter 7: Probability Chance favors prepared minds. -- Louis Pasteur Many decisions that we make involve uncertainty and the evaluation of probabilities. Example: Roll a fair die possible outcomes = { 1, 2, 3, 4, 5, 6 } Before you roll the die do you know which one will occur? No What is the probability that the outcome will be a ‘4’? 1/6 = P(‘4’) Why? A few ways to think about PROBABILITY: (1) Personal or Subjective Probability P(A) = the degree to which a given individual believes that the event A will happen. (2) Long term relative frequency P(A) = proportion of times ‘A’ occurs if the random experiment (circumstance) is repeated many, many times. (3) Basket Model P(A) = proportion of balls in the basket that have an ‘A’ on them. Note: each time I do the experiment, the selected ball is either white or blue; once I look, there is no more ‘probability’) Note: A probability statement IS NOT a statement about INDIVIDUALS . It IS a statement about the population / the basket of balls . 7.3 Probability Definitions and Relationships 7.4 Basic Rules for Finding Probability There is a lot you can learn about probability. One basic rule to always keep in mind is that the probability of any outcome is always between 0 and 1. Now, there are entire courses devoted just to studying probability. But this is a Statistics class. So rather than start with a list of definitions and formulas for finding probabilities, let’s just do it through an example so you can see what ideas about probability we need to know for doing statistics. 10 balls: 3 blue and 7 white; One ball will be selected at random. What is P(blue)? __ 3/10 __
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34 Example: Shopping Online Many Internet users shop online. Consider a population of 1000 customers that shopped online at a particular website during the past holiday season and their results regarding whether or not they were satisfied with the experience and whether or not they received the products on time. These results are summarized below in table form. Using the idea of probability as a proportion, try answering the following questions. On Time Not On Time Total Satisfied 800 20 820 Not Satisfied 80 100 180 Total 880 120 1000 May decide to not include the probability notation P(…) the first time through. a. What is the probability that a randomly selected customer was satisfied with the experience? Think about probability as proportion, so 820/1000 = 0.82 or 82% This would be represented by P(Satisified). b. What is the probability that a randomly selected customer was not satisfied with the experience? Well if 82% were satisfied, then 1 – 0.82 = 0.18 or 18% were not satisfied. Would be represented by P(Not Satisfied), and you just used what we call the complement rule. c. What is the probability that a randomly selected customer was both satisfied
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This note was uploaded on 12/31/2011 for the course STATS 250 taught by Professor Gunderson during the Winter '10 term at University of Michigan.

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Probability complete - Stat 250 Gunderson Lecture Notes...

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