Probability and Venn Diagrams What is a Venn Diagram Venn Diagrams are illustrations used in different

  • View
    0

  • Download
    0

Embed Size (px)

Text of Probability and Venn Diagrams What is a Venn Diagram Venn Diagrams are illustrations used in...

  • Probability and Venn Diagrams

    Coach Whitt

  • Probability and Venn Diagrams

    �What can we say about probability? – It is a measure of likelihood, uncertainty,

    possibility, …

    – And it is a number, numeric measure, between 0 and 1.

    �Simply put: – It is the chance that something will happen.

    �For every event we can carefully assign a number which lies between 0 and 1 inclusive.

  • Experimental vs Theoretical

    Probability � Experimental Probability

    – Determined by observing the results of an experiment.

    • Experimental probability = Number of event occurrences

    Total number of trials

    � Theoretical Probability – The likelihood in an event of what SHOULD happen.

    • Theoretical probability = Number of favorable outcomes

    Total number of outcomes

    � Conditional Probability

    – the probability that event B occurs given that event A has already occurred.

  • Probability Terms

    � Compound Events – made up of two or more simple events.

    • The probability that a flight will be on time and the luggage arrives is an example of a compound event.

    � Dependent Events – 2 or more events whose outcomes affect each other.

    The probability of occurrence of one event depends on the occurrence of the other.

    � Independent Events – 2 or more events whose outcomes do not affect each

    other.

  • Probability Terms

    � Mutually Exclusive Events – 2 outcomes or evens are mutually exclusive when they

    cannot both occur simultaneously.

    � Mutually Inclusive Events – 2 outcomes or events are mutually inclusive when they

    can both occur simultaneously.

    � Outcome – The possible results after a number trials in an

    experiment.

  • What is a Venn Diagram

  • What is a Venn Diagram

    � Venn Diagrams are illustrations used in different branches of mathematics such as Set Theory or Probability.

    � They show the mathematical or logical relationship between different groups of things (sets).

    � A Venn Diagram shows all the possible logical relations between the sets.

  • Contents

    � Who is credited with discovering Venn Diagrams

    � What does a Venn Diagram look like

    � How to use a Venn Diagram

  • Who created Venn Diagrams � Venn Diagrams are named after

    John Venn, a British philosopher and mathematician who introduced these in 1881.

    � John Venn used the diagrams to illustrate ideas used in logic.

    � A stained glass window in Caius College, Cambridge, where he studied and spent most of his life, commemorates John Venn and represents a Venn Diagram.

  • What does a Venn Diagram look

    like? � The simplest and most common Venn Diagram is made of a

    rectangle and two circles that have an overlapping region. • See picture belowTerms –

    •Sample Space or Universal Set

    (Rectangle)

    • Contains all things being

    considered

    • Represented by the red

    rectangle

    •Sets (Circles)

    • Different groups of things

    being considered

    • The intersecting part of the

    circles contains numbers that

    can be found in both sets

  • Venn Diagram Terms

    � Sample Space – A sample space for an experiment is the set of

    ALL experimental outcomes.

    � Set: – A set is a collection of distinct objects,

    considered as an object in its own right – Example:

    • A class of AQR students • NBA teams • Result of a football game for a team (win, lose, tie) • Outcomes of rolling a die ( 1, 2, 3, 4, 5, 6)

  • Terms

    � Union

    – “A union B” is the set of all elements that are in A, or B, or both.

    A B∪

  • Terms

    A B

    A B∩

    •Intersection

    •“A intersect B” is the set of all

    elements that are in both A and B. A B∩

  • Terms

    � Complement of an event A: AC

    – Includes ALL sample points that are not in a set.

  • Mostly Terrible Movies

  • How to Use a Venn Diagram

    � Venn Diagrams can be used to show relationships between sets of information

    � Each circle represents a set of information

  • Turtles

    Ninjas

    Ninja Turtles

  • • There can be more than 2 circles in a Venn Diagram

    • The more circles (Sets) in a Diagram,

    the more complicated it can be.