AG-Ch-5-Notes-WI10

AG-Ch-5-Notes-WI10 - Chapter 5 Notes Probability in our...

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1 Chapter 5 Notes AG 1/28/2010 Chapter 5 Notes - Probability in our Daily Lives I want to know: What is the chance of _____(something)___ happening in the future? What is my past experience? Does this help me answer this question? What is the probability? (Subjective in some ways if it is pertaining just to my past experience.) What type of decisions do we make based on probabilities? Random Events For random events, the outcome is uncertain o In the short-run, the proportion (%) of times that something happens is highly random o In the long-run, the proportion (%) of times that something happens becomes very predictable Probability quantifies long-run randomness Law of Large Numbers As the number of trials increase, the proportion of occurrences of any given outcome approaches a particular number “in the long run” o For example, as one tosses a die, in the long run 1/6 of the observations will be a 6. See Fig. 5.1 o Casinos always come out ahead because of this law. Probability With random phenomenon(occurrence or happenings), the probability of a particular outcome is the proportion (%) of times that the outcome would occur in a long run of observations (over time) Some basic rules for probability P(E) must always be between 0 and 1 and can include 0 or 1 1 ) ( 0 E P If P(E) = 0 it means the event will never occur If P(E) = 1 it means the event will always occur ) ( E P =1 Example: o When rolling a die, the outcome of “6” has probability = 1/6. In other words, the proportion of times that a 6 would occur in a long run of observations is 1/6. Let us consider how we view probability in our own lives: Probability from Intro Stats by DeVeaux, Velleman, and Bock Snow: After an unusually dry autumn, a radio announcer is heard to say, “Watch out! We’ll pay for these sunny days later on this winter.” Explain what he’s trying to say, and comment on the validity of his reasoning. Cold streak: a batter who had failed to get a hit in seven consecutive times at bat then hits a game-winning home run. When talking to reporters afterward, he says he was very confident that last time at bat because he was “due for a hit”. Comment on his reasoning.
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2 Chapter 5 Notes AG 1/28/2010 Crash: Commercial airplanes have an excellent safety record. Nevertheless, there are crashes occasionally, with the loss of many lives. In the weeks following a crash, airlines often report a drop in the number of passengers; probably because people are afraid to risk flying. A travel agent suggest that, since the law of averages makes it highly unlikely to have two plane crashes within a few weeks of each other, flying soon after a crash is the safest time. What do you think? If the airline industry proudly announces that it has set a new record for the longest period
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This note was uploaded on 05/18/2010 for the course MATH math 208 taught by Professor C.eckerle during the Winter '10 term at Delta MI.

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AG-Ch-5-Notes-WI10 - Chapter 5 Notes Probability in our...

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