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Probability By: Alex von Ebers and Lyndsi Monjon Probability Defined • Probability is the relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible outcomes (dictionary.com). • Our Definition – the chance that one specific outcome will happen out of multiple options. Theoretical Probability • Theoretical probability is when you can get the probability but you can’t be absolutely sure that the subject is fair to both sides. • For example, the probability of a coin landing on heads is fifty percent. This is only true if the coin is fair, and we are able to assume that the coin has an equal chance to land on heads or tails. Empirical Probability • Empirical probability is when you find a probability based on experiments and observations (Bennett 432). • An example of this is if you had five earthquakes in the last forty years. The probability that you could have an earthquake the next year is .125 or about one earthquake in every eight years. Subjective Probability • Subjective probabilities are when you make an estimate based on past experiences or intuition (Bennett 435). • An example of that would be if someone was to say that they are seventy-five percent sure that you are going to get in a car crash in the next year. This is a subjective probability because they are basing this on their experiences with you and their intuition. History • Many of the mathematicians who first developed the theory of probability were gamblers (Vorderman 79). • A gambler’s dispute in 1654 led to the creation of a mathematical theory of probability (Apostol). History Continued • No general theory was developed before a famous correspondence between two French men, Blaise Pascal and Pierre de Fermat (Apostol). • In 1657, Dutch scientist, Christian Huygens wrote the first book on probability (Apostol). More History • It was not until the twentieth century that a definition was decided on because it was hard to find something good enough for mathematics, yet comprehensive enough to be applicable to a wide range of phenomena (Apostol). How to Find Theoretical Probability 1) Count the total number of possible outcomes 2) Among all the possible outcomes, count the number of ways the event of interest, A, can occur. 3) Determine the probability , P(A), from the following equation P(A)= number of ways A can occur total number of outcomes How to Find Empirical Probability 1) Find the number of observed events. 2) Divide that by the amount of time or total number of events. How to Find Subjective Probability • No formal equation for subjective probability. • Based off of experience and/or intuition. • Knowing the three types of Probability, which one would you use to figure out the probability of picking a certain color of skittle? Probability and Everyday Life • Gambling/Games of Chance • Medical Checks • Sports • Pregnancy – Date of Birth – Gender – Genetics Activities • Flipping a coin • Rolling Dice • Chance of Rain • Rock, Paper, Scissors Skittles • We are going to find the probability of reaching into a bag and pulling out a specific color skittle. • We will figure the probability of grabbing each color. Activity • Count each color of skittle • Record on sheet • Add up each number to find the total • Write down the percentage of getting each color. Small Bag • Red: 14 skittles, 23.3% • Orange: 12 skittles, 20% • Yellow: 15 skittles, 25% • Green: 9 skittles, 15% • Purple: 10 skittles, 16.7% • Total: 60 skittles Big Bag • Red: 102 skittles, 24.4% • Orange: 61 skittles, 14.6% • Yellow: 129 skittles, 30.9% • Green: 66 skittles, 15.8% • Purple: 60 skittles, 14.4% • Total: 418 skittles Comparing Your Results • Total number of skittles per bag • Each Color Works Cited • Apostol, Tom M. A Short History of Probability. 1969. 20 Nov. 2006 <http://www.cc.gatech.edu/classes/cs6751_97_winter/Topics/stat- meas/probHist.html>. • Bennett, Jeffrey, and William Briggs. Using and Understanding Mathematics: a Quantitative Reasoning Approach. 3rd ed. Boston: Greg Tobin, 2005. 430-451. • Littlefield, Cindy A. Real-World Math for Hands-on Fun! Charlotte: Williamson, 2001. 90-100. • Packel, Edward. The Mathematical Game of Gambling. Washington: The Mathematical Association of America, 1981. 20-62. • "Probability." Dictionary.Com. 28 Nov. 2006 • The Probability in Everyday Life. 27 Nov. 2006 <http://media.wiley.com/product_data/excerpt/13/04717514/0471751413.pd f>. • Vorderman, Carol. How Math Works. Pleasantville: Reader_Digest, 1996. 69-81.