Probability by opza81

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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.

								
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