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Chapter 3 Notes

Chapter 3 Notes - Probability and Statistics Notes on...

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Probability and Statistics Notes on Chapter 3: Probability Section 3.1: Basic Concepts of Probability Uses of Probability: Probability affects decisions when the weather is forecast, when marketing strategies are determined, insurance, investments, when medications are selected, winning a lottery/raffle/bet, and when players are selected for professional sports teams, etc. Probability is the basis of inferential statistics, which grew out of using coins, dice and cards. These types of things were found in pyramids. One abuse is to assume probabilities have “memories.” Throwing a coin has no memory of what is landed on previously. Another common abuse is to incorrectly add probabilities. History : During the mid-1600s, a professional gambler made a lot of money on a gambling game, he devised a new game and could not win so he contacted a mathematician Blaise Pascal (1632-1692. Pascal became interested and began to study probability, he corresponded with Pierre de Fermat (1601-1695), and the two formulated the beginnings of probability theory. Pierre Laplace (1749-1827) studied probability and is credited with putting probability on a sure mathematical footing. The first book written on probability, The Book of Chance and Games, was written by Jerome Cardan (1501 – 1575). Cardan was an astrologer, philosopher, physician, mathematician, and gambler. This book contained techniques on how to cheat and how to catch others at cheating. Probability experiment: an action or trial through which specific results are obtained. Example: Roll a die, flip a coin, or draw a card from a deck. **Probability can be expressed as fractions (reduce), decimals (round to two or three decimal places) or percentages. ** Outcome: result of single trial in a probability experiment. Example: Roll a die, and get a 4. Flip a coin and get heads. Sample space: set of all possible outcomes of a probably experiment. Example: Roll a die and get a 1 or 2 or 3 or 4 or 5 or 6. Flip a coin and get either a Head or Tail.
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