M408 Probability Unit. Example 1 –  You have a six-sided die with faces of 1, 2, 3, 4, 5, and 6. If you roll the die several times, what would you expect.

Slides:

Advertisements

Similar presentations

Expected Value. When faced with uncertainties, decisions are usually not based solely on probabilities A building contractor has to decide whether to.

Advertisements

Stat 245 Recitation 13 11/1/2007 EA :30am TA: Dongmei Li.

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide

Clear your desk for your quiz. Unit 2 Day 8 Expected Value Average expectation per game if the game is played many times Can be used to evaluate and.

6.2 Construct and Interpret Binomial Distributions

Binomial Distributions

TODAY IN GEOMETRY…  Warm Up  Learning Goal: You will find the probability for event given in a two-way table  Independent practice.

EXAMPLE 1 Construct a probability distribution

PROBABILITY  A fair six-sided die is rolled. What is the probability that the result is even?

EXAMPLE 1 Construct a probability distribution Let X be a random variable that represents the sum when two six-sided dice are rolled. Make a table and.

Random Variables A Random Variable assigns a numerical value to all possible outcomes of a random experiment We do not consider the actual events but we.

Chapter 5 Discrete Probability Distributions © McGraw-Hill, Bluman, 5 th ed, Chapter 5 1.

Binomial PDF and CDF Section Starter Five marbles are on a table. Two of them are going to be painted with a “W” and the rest will be painted.

Refreshing Your Skills for Chapter 10.  If you flip a coin, the probability that it lands with heads up is 1/2.  If you roll a standard die, the probability.

An outcome is a possible result An event is a specific outcome Random means all outcomes are equally likely to occur or happen. random = fair A favorable.

McGraw-Hill/IrwinCopyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved. Chapter 4 and 5 Probability and Discrete Random Variables.

Discrete Probability Distributions

Unit 5 Section : Mean, Variance, Standard Deviation, and Expectation  Determining the mean, standard deviation, and variance of a probability.

Lesson 12-6 Pages Counting Outcomes. What you will learn! 1. How to use tree diagrams or the Fundamental Counting Principle to count outcomes.

Probability Distributions Random Variables * Discrete Probability Distributions * Mean, Variance, and Standard Deviation * Expected Value.

Chapter 7: Probability Lesson 6: Probability Distributions Mrs. Parziale.

 5-1 Introduction  5-2 Probability Distributions  5-3 Mean, Variance, and Expectation  5-4 The Binomial Distribution.

Chapter 2 - Probability 2.1 Probability Experiments.

Probability Distributions. We need to develop probabilities of all possible distributions instead of just a particular/individual outcome Many probability.

Chapter 5 Discrete Probability Distributions. Random Variable A numerical description of the result of an experiment.

Course schedule: continue We finished 3.2, but we’ll do a couple practice problems. Section 3.3: Grouped data.

MM1D2d: Use expected value to predict outcomes

©The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin A Survey of Probability Concepts Chapter 5.

Not So Great Expectations! Which game do you think has the highest return per dollar?

Math I.  Probability is the chance that something will happen.  Probability is most often expressed as a fraction, a decimal, a percent, or can also.

Theoretical Probability WORDS: The ratio of the number of ways the event can occur to the number of possible outcomes. SYMBOLS: number of ways the event.

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.

L56 – Discrete Random Variables, Distributions & Expected Values

Mean, Median, Mode, and Range. 2 Lesson Mean, Median, and Mode California Standard: Statistics, Data Analysis, and Probability 1.1 Compute the range,

Lesson Discrete Random Variables. Objectives Distinguish between discrete and continuous random variables Identify discrete probability distributions.

Chapter 5 Discrete Probability Distributions 1 Copyright © 2012 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Nick Bulinski.  A six-sided die (whose faces are numbered 1 through 6, as usual) is known to be counterfeit: The probability of rolling any even number.

+ Chapter 5 Probability: What Are the Chances? 5.1Randomness, Probability, and Simulation 5.2Probability Rules 5.3Conditional Probability and Independence.

Chapter 9 Section 7 Chapter 12 Section 2 Algebra 2 Notes February 12, 2009.

Chapter 10 – Data Analysis and Probability 10.7 – Probability of Compound Events.

The Mean of a Discrete Random Variable Lesson

Copyright © 2009 Pearson Education, Inc. Chapter 12 Section 2 - Slide 1 P-2 Probability Theoretical Probability.

Find Expected Value.  A collection of outcomes is partitioned into n events, no two of which have any outcomes in common. The probabilities of n events.

Probability and Simulation The Study of Randomness.

Probability Distributions Table and Graphical Displays.

Probability Distributions. Constructing a Probability Distribution Definition: Consists of the values a random variable can assume and the corresponding.

Probability. Today we will look at… 1.Quick Recap from last week 2.Terminology relating to events and outcomes 3.Use of sample spaces when dealing with.

In games of chance the expectations can be thought of as the average outcome if the game was repeated multiple times. Expectation These calculated expectations.

Chapter 8: The Binomial and Geometric Distributions 8.2 – The Geometric Distributions.

Discrete Probability Distributions Chapter 5 1. Chapter 5 Overview 2 Introduction 5-1 Probability Distributions 5-2 Mean, Variance, Standard Deviation,

FTCE 5-9 Test Prep Center for Teaching and Learning.

Chapter5 Statistical and probabilistic concepts, Implementation to Insurance Subjects of the Unit 1.Counting 2.Probability concepts 3.Random Variables.

Bell Ringer The P(A), you showing up to school on time, is 0.8. The P(B), you completing your homework, is 0.7. Are events A and B independent if the.

Probability of Independent Events

Stats 4 Day 20b.

Probability Distribution

CHAPTER 6 Random Variables

Discrete Probability Distributions

Chapter 3.1 Probability Students will learn several ways to model situations involving probability, such as tree diagrams and area models. They will.

Chapter 3.1 Probability Students will learn several ways to model situations involving probability, such as tree diagrams and area models. They will.

Secondary Math Venn Diagrams – and/or.

10.1 Notes Need to grab a packet from the back for notes

Probability Key Questions

Probability The risk of getting struck by lightning in any year is 1 in 750,000. The chances of surviving a lightning strike are 3 in 4. These risks.

U10D3 Have out: Bellwork: Work on the Probability Practice Worksheet.

Section 12.2 Theoretical Probability

Section 12.2 Theoretical Probability

e is the possible out comes for a model

Section 12.2 Theoretical Probability

Presentation transcript:

M408 Probability Unit

Example 1 –  You have a six-sided die with faces of 1, 2, 3, 4, 5, and 6. If you roll the die several times, what would you expect the average of your rolls to be?

Example 2 –  Suppose you have a ‘loaded’ die. It is designed such that the number ‘6’ appears 1/3 of the time, a ‘5’ appears 1/3 of the time, and 1, 2, 3, 4 have equal chances of appearing.  If you roll the die several times, what would you expect the average of your rolls to be?

 Must involve numerical outcomes.  Multiply each outcome by its probability.  Add all the products.  Represents a ‘weighted’ average (after several trials).  Sum of probabilities = 1

Example 3 – In four years at Fremd, you got an A in 15% of your classes, a B in 30% of your classes, a C in 40%, a D in 10%, and an F in 5% of your classes. What is your GPA? (When calculating GPA, A = 4, B = 3, C = 2, D = 1, F = 0)

Example 4 – The table shows the number of siblings that students have, based on a survey. What is the average number of siblings for respondents in this survey? Number of Siblings Number of Respondents

Example 5 – You took a survey, asking “How many hours of homework do you do each night?” You lost some of the data! Can you still determine the expected number of hours of homework done each night? Number of hours of homework Percent of those surveyed 31?251612

Example 6 – I have 20 gift cards. I am selling them for three dollars each. Two of the cards have $20 value, five of the cards have $10 value, and the rest have no money. If you buy a gift card from me, what is your expected net monetary gain?