Introduction to Probability (Dr. Monticino) - PowerPoint PPT Presentation

About This Presentation
Title:

Introduction to Probability (Dr. Monticino)

Description:

Title: Introduction to Decision Analysis Subject: Decision Analysis Author: Michael Monticino Description: Course to Denton Utilities Last modified by – PowerPoint PPT presentation

Number of Views:92
Avg rating:3.0/5.0
Slides: 12
Provided by: Michael3975
Learn more at: http://www.math.unt.edu
Category:

less

Transcript and Presenter's Notes

Title: Introduction to Probability (Dr. Monticino)


1
Introduction to Probability
(Dr. Monticino)
2
Assignment Sheet
  • Read Chapters 13 and 14
  • Assignment 8 (Due Wednesday March 23rd )
  • Chapter 13
  • Exercise Set A 1-5 Exercise Set B 1-3
  • Exercise Set C 1-4,7 Exercise Set D 1,3,4
  • Review Exercises 2,3, 4,5,7,8,9,11
  • Chapter 14
  • Exercise Set A 1-4 Exercise Set B 1-4, 5
  • Exercise Set C 1,3,4,5 Exercise Set D 1
    (just calculate probabilities)
  • Review Exercises 3,4,7,8,9,12

3
Overview
  • Framework
  • Equally likely outcomes
  • Some rules

4
Probability Framework
  • The sample space, ?, is the set of all outcomes
    from an experiment
  • A probability measure assigns a number to each
    subset (event) of the sample space, such that
  • 0 ? P(A) ? 1
  • P(? ) 1
  • If A and B are mutually exclusive (disjoint)
    subsets, then P(A ? B) P(A) P(B) (addition
    rule)

5
Equally Likely Outcomes
  • Outcomes from an experiment are said to be
    equally likely if they all have the same
    probability.
  • If there are n outcomes in the experiment then
    the outcomes being equally likely means that each
    outcome has probability 1/n
  • If there are k outcomes in an event, then the
    event has probability k/n
  • Fair is often used synonymously for equally
    likely

6
Examples
  • Roll a fair die
  • Probability of a 5 coming up
  • Probability of an even number coming up
  • Probability of an even number or a 5
  • Roll two fair die
  • Probability both come up 1 (double ace)
  • Probability of a sum of 7
  • Probability of a sum of 7 or 11

7
More Examples
  • Spin a roulette wheel once
  • Probability of 11
  • Probability of red probability of black
    probability of not winning if bet on red
  • Draw one card from a well-shuffled deck of cards
  • Probability of drawing a king
  • Probability of drawing heart
  • Probability of drawing king of hearts

8
Conditional Probability
  • All probabilities are conditional
  • They are conditioned based on the information
    available about the experiment
  • Conditional probability provides a formal way for
    conditioning probabilities based on new
    information
  • P(A B) P(A ? B)/P(B)
  • P(A ? B) P(A B) ? P(B)

9
Multiplication Rule
  • The probability of the intersection of two events
    equals the probability of the first multiplied by
    the probability of the second given that the
    first event has happened
  • P(A ? B) P(A B) ? P(B)

10
Examples
  • Suppose an urn contains 5 red marbles and 8 green
    marbles
  • Probability of red on first draw
  • Red on second, given red on first (no
    replacement)
  • Red on first and second

11
Independence
  • Intuitively, two events are independent if
    information that one occurred does not affect the
    probability that the other occurred
  • More formally, A and B are independent if
  • P(A B) P(A)
  • P(B A) P(B)
  • P(A?B) P(A)P(B)

  • (Dr. Monticino)
Write a Comment
User Comments (0)
About PowerShow.com