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Chapter14

# Chapter14 - Chapter 14(From Randomness to Probability A...

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1 Chapter 14 (From Randomness to Probability) A roulette wheel contains 38 slots, 18 of which are red, 18 are black, and two are green. If you were planning to bet \$5, what color should you bet on? It’s impossible to know. Assuming the game is fair, the outcome of any one spin is completely unpredictable. However, after many thousands of spins we see that the percentage of times the ball lands in a red spot is a predictable number. This predictable value is called a probability . (there’s an interesting example on page 365 regarding red versus green lights) The study of probability is used to mathematically describe what we should expect to happen if an experiment were repeated many times. In effect, probability is used to describe long-term behavior (Law of Large Numbers – see pages 366-367 & graph on pg. 365). It is the proportion of times a given outcome occurs in many independently repeated trials . (See Jacob Bernoulli’s quote on page 367) What is the probability of the roulette ball landing on red on any given spin? P(red) = What does it mean to say that spins of the roulette wheel are independent of each other? A common mistake made when working with probability is to confuse the Law of Large Numbers with the Law of Averages . There is no such thing as a Law of Averages (it’s a fallacy – see pg. 367-368). An interesting scenario about Keno and the Law of Averages is given on page 368 – these grad students “beat the system” for \$50,000 because the Keno game was not completely random (outcomes were predictable) A quote from page 367: Don’t let yourself think that there’s a Law of Averages that promises short-term compensation for recent deviations from expected behavior. A belief in such a “Law” can lead to money lost in gambling and poor business decisions. Activity 1: Dr. Fidget developed a test to measure boredom tolerance. He administered it to a group of 200 adults between the ages of 25 and 35. The possible scores were 0, 1, 2, 3, 4, 5, and 6, with 6 indicating the highest tolerance for boredom (listen for 75 minutes without getting bored). The results are shown below.

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Chapter14 - Chapter 14(From Randomness to Probability A...

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