Dr. Fowler  AFM  Unit 7-8 Probability.

Slides:



Advertisements
Similar presentations
Beginning Probability
Advertisements

Copyright © 2010, 2007, 2004 Pearson Education, Inc. Chapter 14 From Randomness to Probability.
Probability & Counting Rules Chapter 4 Created by Laura Ralston Revised by Brent Griffin.
Chapter 3 Probability.
Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc. Chap 4-1 Business Statistics: A Decision-Making Approach 7 th Edition Chapter.
Probability.
Sect.3-1 Basic Concepts of Probability
Probability Chapter 3. § 3.1 Basic Concepts of Probability.
Copyright © 2015, 2011, 2008 Pearson Education, Inc. Chapter 7, Unit A, Slide 1 Probability: Living With The Odds 7.
Elementary Probability Theory
Conditional Probability
Probability. An experiment is any process that allows researchers to obtain observations and which leads to a single outcome which cannot be predicted.
Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 12.6 OR and AND Problems.
Probability Section 7.1.
Probability. Basic Concepts of Probability and Counting.
Chapter 7 Probability. 7.1 The Nature of Probability.
Basic Concepts of Probability Coach Bridges NOTES.
Copyright © 2010 Pearson Education, Inc. Chapter 14 From Randomness to Probability.
 Probability: the chance that a particular event will occur.  When do people use probability ◦ Investing in stocks ◦ Gambling ◦ Weather.
Advanced Precalculus Advanced Precalculus Notes 12.3 Probability.
From Randomness to Probability Chapter 14. Dealing with Random Phenomena A random phenomenon is a situation in which we know what outcomes could happen,
Probability Basics Section Starter Roll two dice and record the sum shown. Repeat until you have done 20 rolls. Write a list of all the possible.
Dr. Fowler AFM Unit 7-8 Probability. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Example Suppose we roll a die and flip a coin. How many possible outcomes are there? Give the sample space. A and B are defined as: A={Die is a 5 or 6}
Chapter 12 Section 1 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
Probability Chapter 3. § 3.1 Basic Concepts of Probability.
Unit 4 Section 3.1.
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 11 Counting Methods and Probability Theory.
Chapter 6 - Probability Math 22 Introductory Statistics.
Probability 9.8. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Definition: Experiment Any activity with an unpredictable results.
Probability. Definitions Probability: The chance of an event occurring. Probability Experiments: A process that leads to well- defined results called.
Introduction to probability (3) Definition: - The probability of an event A is the sum of the weights of all sample point in A therefore If A1,A2,…..,An.
Discrete Math Section 16.1 Find the sample space and probability of multiple events The probability of an event is determined empirically if it is based.
Fundamentals of Probability
Probability II.
12.3 Probability of Equally Likely Outcomes
Probability and Sample Space…….
Probability and Counting Rules
Essential Ideas for The Nature of Probability
Mathematics Department
From Randomness to Probability
PROBABILITY Probability Concepts
Basic Business Statistics (8th Edition)
Chapter 4 Probability Concepts
Copyright © 2016, 2013, and 2010, Pearson Education, Inc.
Definitions: Random Phenomenon:
Introduction to Probability
From Randomness to Probability
A Survey of Probability Concepts
From Randomness to Probability
CHAPTER 4 (Part A) PROBABILITY
Elementary Statistics: Picturing The World
Elementary Statistics: Picturing The World
6.2 Basics of Probability LEARNING GOAL
Probability: Living with the Odds
PROBABILITY.
Section 3-3 Mutually exclusive events are events that cannot both happen at the same time. The Addition Rule (For “OR” probabilities) “Or” can mean one.
Chapter 3 Probability.
Chapter 3 Probability.
Section 6.2 Probability Models
Chapter 4 Section 1 Probability Theory.
CHAPTER 4 PROBABILITY Prem Mann, Introductory Statistics, 8/E Copyright © 2013 John Wiley & Sons. All rights reserved.
6.2 Basics of Probability LEARNING GOAL
Digital Lesson Probability.
Additional Rule of Probability
Section 12.6 OR and AND Problems
6.1 Sample space, events, probability
Chapter 4 Probability.
Chapter 4 Lecture 3 Sections: 4.4 – 4.5.
Exponential Functions
Presentation transcript:

Dr. Fowler  AFM  Unit 7-8 Probability

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Introduction to Probability: https://www.youtube.com/watch?v=YWt_u5l_jHs

Classical Probability Classical (or theoretical) probability is used when each outcome in a sample space is equally likely to occur. P(Event) = the favorable number of outcomes the number of possible outcomes Example: A die is rolled. Find the probability of Event A: rolling a 5. There is one outcome in Event A: {5} P(A) = “Probability of Event A.”

Empirical Probability Empirical (or statistical) probability is based on observations obtained from probability experiments. The empirical frequency of an event E is the relative frequency of event E. Example: A travel agent determines that in every 50 reservations she makes, 12 will be for a cruise. What is the probability that the next reservation she makes will be for a cruise? P(cruise) =

Definition – a probability model will always have: 1) positive values & 2) total values adding up to 1

S = 8 Total outcomes listed Calculate the probability that in a 3 child family there are 2 boys and 1 girl. Assume equally likely outcomes. E = All outcomes with 2 Boys & 1 Girl = { BBG, BGB, GBB } = 3 Total S = 8 Total outcomes listed

The Addition Rule – Mutually Exclusive Example: You roll a die. Find the probability that you roll a number less than 3 or a 4. The events are mutually exclusive. P (roll a number less than 3 or roll a 4) = P (number is less than 3) + P (4)

The Addition Rule – Not Mutually Exclusive Example: A card is randomly selected from a deck of cards. Find the probability that the card is a Jack or the card is a heart. The events are not mutually exclusive because the Jack of hearts can occur in both events. P (select a Jack or select a heart) = P (Jack) + P (heart) – P (Jack of hearts)

Complementary Events The complement of Event E is the set of all outcomes in the sample space that are not included in event E. (Denoted E′ and read “E prime.”) P(E) + P (E′ ) = 1 P(E) = 1 – P (E′ ) P (E′ ) = 1 – P(E) Example: There are 5 red chips, 4 blue chips, and 6 white chips in a basket. Find the probability of randomly selecting a chip that is not blue. P (selecting a blue chip) P (not selecting a blue chip)

On the local news the weather reporter stated that the probability of rain tomorrow is 30%. What is the probability that it will not rain?

Multiplication Rule Example: A die is rolled and two coins are tossed. Find the probability of rolling a 5, and flipping two tails. P (rolling a 5) = Whether or not the roll is a 5, P (Tail ) = so the events are independent. P (5 and T and T ) = P (5)· P (T )· P (T )

Notice – sum of probabilities is 1

Notice – sum of probabilities is 1

What is the probability that in a group of 10 people at least 2 people have the same birthday? Assume that there are 365 days in a year.

Excellent Job !!! Well Done