Download presentation

Presentation is loading. Please wait.

Published byZayne Chesser Modified over 2 years ago

1
Introduction to Probability Experiments, Outcomes, Events and Sample Spaces What is probability? Basic Rules of Probability Probabilities of Compound Events

2
Experiments, Outcomes, Events and Sample Spaces Experiment: An experiment is any activity from which results are obtained. A random experiment is one in which the outcomes, or results, cannot be predicted with certainty. Examples: 1.Flip a coin 2.Flip a coin 3 times 3.Roll a die 4.Draw a SRS of size 50 from a population Trial: A physical action, the result of which cannot be predetermined

3
Basic Outcomes and Sample Spaces Basic Outcome (o): A possible outcome of the experiment Sample Space: The set of all possible outcomes of an experiment Example: A company has offices in six cities, San Diego, Los Angeles, San Francisco, Denver, Paris, and London. A new employee will be randomly assigned to work in on of these offices. Outcomes: Sample Space:

4
Example #2: A random sample of size two is to be selected from the list of six cities, San Diego, Los Angeles, San Francisco, Denver, Paris, and London. Outcomes: Sample Space:

5
Events and Venn Diagrams Events: Collections of basic outcomes from the sample space. We say that an event occurs if any one of the basic outcomes in the event occurs. Example #1 (cont.): 1.Let B be the event that the city selected is in the US 2.Let A be the event that the city selected is in California Venn Diagram: Graphical representation of sample space and events

6
Example #2: A random sample of size two is to be selected from the list of six cities, San Diego, Los Angeles, San Francisco, Denver, Paris, and London. Let E be the event that both cities selected are in the US E= Sample Space and Venn Diagram:

7
Assigning Probabilities to Events Probability of an event P(E): “Chance” that an event will occur Must lie between 0 and 1 “0” implies that the event will not occur “1” implies that the event will occur Types of Probability: Objective Relative Frequency Approach Equally-likely Approach Subjective

8
Relative Frequency Approach: Relative frequency of an event occurring in an infinitely large number of trials Equally-likely Approach: If an experiment must result in n equally likely outcomes, then each possible outcome must have probability 1/n of occurring. Examples: 1.Roll a fair die 2.Select a SRS of size 2 from a population Subjective Probability: A number between 0 and 1 that reflects a person’s degree of belief that an event will occur Example: Predictions for rain

9
Odds If the odds that an event occurs is a:b, then Example: If the odds of Came Home winning the Derby are 9:2, what is the subjective probability that he will win?

10
Probabilities of Events Let A be the event A = {o 1, o 2, …, o k }, where o 1, o 2, …, o k are k different outcomes. Then Problem 5.3.4: The number on a license plate is any digit between 0 and 9. What is the probability that the first digit is a 3? What is the probability that the first digit is less than 4?

11
Law of Complements: “If A is an event, then the complement of A, denoted by, represents the event composed of all basic outcomes in S that do not belong to A.” Additive Law of Probability: Probabilities of Compound Events A S

12
“If A is an event, then the complement of A, denoted by, represents the event composed of all basic outcomes in S that do not belong to A.” Law of Complements A S Law of Complements: Example: If the probability of getting a “working” computer is ).7, What is the probability of getting a defective computer?

13
Unions of Two Events “If A and B are events, then the union of A and B, denoted by A B, represents the event composed of all basic outcomes in A or B.” Intersections of Two Events “If A and B are events, then the intersection of A and B, denoted by A B, represents the event composed of all basic outcomes in A and B.” Unions and Intersections of Two Events S B A

14
Additive Law of Probability Let A and B be two events in a sample space S. The probability of the union of A and B is S B A

15
Using Additive Law of Probability S B A Example: At State U, all first-year students must take chemistry and math. Suppose 15% fail chemistry, 12% fail math, and 5% fail both. Suppose a first-year student is selected at random. What is the probability that student selected failed at least one of the courses?

16
Mutually Exclusive Events Mutually Exclusive Events: Events that have no basic outcomes in common, or equivalently, their intersection is the empty set. S B A Let A and B be two events in a sample space S. The probability of the union of two mutually exclusive events A and B is

17
Multiplication Rule and Independent Events Multiplication Rule for Independent Events: Let A and B be two independent events, then Examples: Flip a coin twice. What is the probability of observing two heads? Flip a coin twice. What is the probability of getting a head and then a tail? A tail and then a head? One head? Three computers are ordered. If the probability of getting a “working” computer is.7, what is the probability that all three are “working” ?

Similar presentations

OK

Lecture 7 Dustin Lueker. Experiment ◦ Any activity from which an outcome, measurement, or other such result is obtained Random (or Chance) Experiment.

Lecture 7 Dustin Lueker. Experiment ◦ Any activity from which an outcome, measurement, or other such result is obtained Random (or Chance) Experiment.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on earth hour 2017 Ppt on mauryan architecture Ppt on power supply failure alarm Ppt on interview skills training Ppt on 21st century skills teacher Ppt on different solid figures shapes Helmet mounted display ppt online Ppt on autonomous car technology A ppt on amelia earhart Ppt on measurement of price elasticity of demand