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Probability theory. Chapter 14 sec 1. Movie Quotes.

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Probability theory

Probability theory

Chapter 14 sec 1


Movie quotes
Movie Quotes

  • "In this galaxy, there's a mathematical probability of three million Earth type planets.  And in all of the universe three million, million galaxies like this.  And in all of that, and perhaps more, only one of each of us.  Don't destroy the one named 'Kirk.'"


  • Kirk: Mr. Spock, have you accounted for the variable mass of whales and water in your time re-entry program? Spock: Mr. Scott cannot give me exact figures, Admiral, so... I will make a guess. Kirk: A guess? You, Spock? That's extraordinary.


Famous quotes
Famous quotes

  • AristotleThe probable is what usually happens.

  • Bertrand, JosephCalcul des probabilitésHow dare we speak of the laws of chance? Is not chance the antithesis of all law?


  • Joseph Louis François Bertrand (March 11, 1822 – April 5, 1900, born and died in Paris) was a Frenchmathematician who worked in the fields of number theory, differential geometry, probability theory, economics and thermodynamics.


  • Caesar, JuliusIactaalea est. (The die is cast.)

  • Doyle, Sir Arthur ConanThe Sign of FourWhen you have eliminated the impossible, what ever remains, however improbable, must be the truth.


Random phenomena
Random phenomena

  • What is random phenomena?

    • Occurrences that vary from day to day and case to case.

    • Weather conditions, rolling dice at craps or Monopoly, drilling oil, driving your car.

    • We never know exactly how a random phenomena will turn out, we often can calculate a number called probability.


Experiment
Experiment

  • Def.

    • Is any observation of a random phenomenon.


Outcome
Outcome

  • Def.

    • The different possible results of the experiment


Sample space
Sample Space

  • Def.

    • The set of all possible outcomes for an experiment.


Finding the sample space example 1
Finding the sample space.Example 1

  • We select an iPhone from a production line and determine whether it is defective.

  • The sample space is;

    • {defective, nondefective}


Example 2
Example 2

  • Three children are born to a family and we note the birth order with respect to gender.

  • Make a tree diagram and find all the possibilities.

    • {bbb,bbg,bgg,bgb,gbb,gbg, ggb,ggg}


Event
Event

  • Def.

    • In probability theory, an event is a subset of the sample space.


Write each event as a subset of the sample space
Write each event as a subset of the sample space.

  • A tails occurs when we flip a single coin.

  • {Tails}

  • Two girls and one boy are born in a family.

  • {ggb,gbg,bgg}


Probability of an outcome
Probability of an outcome

  • Def.

    • In a sample space is an number between 0 and 1 inclusive. The sum of the probabilities of all the outcomes in the sample space must be 1.


Certain

1.0

Likely to occur

0.5

50-50 Chance of occurring

Not likely to occur

Impossible

0.0


Probability of an event e
Probability of an event (E)

  • Def.

    • P(E) is defined as the sum of the probabilities of the outcome that make up E.



Empirical assignment of probabilities
Empirical assignment of Probabilities information. Meaning we make observations and assign probabilities based on those observations.

  • If E is an event and we perform an experiment several times, then we estimate the probability of E as follows;


Formula
Formula information. Meaning we make observations and assign probabilities based on those observations.



Table
Table divided over the proposed construction of a spring car racetrack in the town.


Problem
Problem divided over the proposed construction of a spring car racetrack in the town.

  • If a newspaper reporter randomly selects a person to interview from these people,

    • What is the probability that the person supports the racetrack?



Cal probability when outcomes are equally likely
Cal. Probability when outcomes are equally likely. racetrack?

  • If E is an event in a sample space S with all equally likely outcomes, then the probability of E is given by the formula;


Computing probability of events
Computing Probability of Events racetrack?

  • What is the probability in a family with three children that two of the children are girls?

  • Using example 2 that there are eight outcomes in the sample set. G={ggb,gbg,bgg}





Basic properties of probability
Basic Properties of Probability roll two fair dice?

  • Assume that S is a sample space for some experiment and E is an event in S.

    • 1)

    • 2)

    • 3)


Probability formula for computing odds
Probability formula for computing odds roll two fair dice?

  • If E’ is the complement of the event E, then the odds against E are


Example problem
Example problem roll two fair dice?

  • Suppose that the probability of the Saints winning the Super Bowl is 0.15. What are the odds against the Saints winning the Super Bowl.


  • 1-0.15 = 0.85 roll two fair dice?

  • This answer is the complement, P(E’)

  • 0.15 is the probability of E, P(E)

  • The odds against the Saints are



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