The myth of short-run regularity Ch 5 - Probability Think about this: Which is more likely to happen if I flipped a coin 6 times TTHHTH HHHTTT The myth of short-run regularity Date

Probability The probability of any outcome of a chance process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of repetitions. For each of the following probabilities, give an event that corresponds to that probability. 0 – 0.1 – 0.25 – 0.5 – 0.8 – 0.99 – 1 -

Probability is a predicted long-run frequency According to thebookofodds.com The odds a woman will attend an NFL game in a year are 1 in 18.83 The odds a golfer will make two consecutive holes in one are about 1 in 156,000,000, a bit better than winning powerball The odds a man 25 - 29 will die in a year are 1 in 721 The odds a baby born in the US will be part of a multiple delivery are 1 in 29.7 The odds a person will be injured by lightning in a year are 1 in 2,183,000 The odds a woman owns a firearm are 1 in 9.09 The odds a driver will be stopped by the police in a year are 1 in 11.48 The odds an American is a grandparent are 1 in 4.4—the same odds an adult 18 - 44 is obese (1 in 4.4), or an adult will play cards in a year (1 in 4.4) The odds a person has health insurance are 1 in 1.18

You read in a poker book that the probability of getting a pair is 88/1000. Explain what this means.

Why do they charge what they do? According to the CDC, the probability a male between 20-24 will die within a year is 0.0015 and for a woman it is 0.0005. How much should a life insurance company charge?

The Law of Averages MYTH! A couple has two sons and decides to have a third child. One spouse says, “We’re bound to have a daughter this time: things balance out.” The other says, “Nonsense! Two boys in a row mean we are more likely to have another boy.” Who is correct? Defend your answer. MYTH!

Only one of the below definitions is mathematically dependable Only one of the below definitions is mathematically dependable. Which one is correct? Justify your answer. The _____________________ says that a certain outcome becomes more likely to occur if the opposite outcome has occurred several times in a row. The _______________________ says that if we observe more and more repetitions of any chance process, the proportion of times that a specific outcome occurs approaches a single value.

Example A gambler knows that red and black are equally likely to occur on each spin of a roulette wheel. He observes five consecutive reds occur and wants to know what he should bet on the next spin. What should you tell him? Justify your answer. A – Bet red because it’s lucky right now and red is more likely to occur than black B – Bet black because there have been a lot of reds and it’s time for black C – Black and red are still equally likely to occur on the next spin

Drug tests are not perfect Drug tests are not perfect. Sometimes they can show a false positive or a false negative. What is a false positive? What is a false negative? What would it be called if the test accurately showed a positive drug use result? Which is more serious? For whom? Why?