Probability. Discussion Topics  Conditional Probability  Probability using the general multiplication rule  Independent event.

Slides:

Advertisements

Similar presentations

Section 6.3 Probability Models Statistics AP Mrs. Skaff.

Advertisements

Conditional Probability Target Goal: I can find the probability of a conditional event. 5.3b h.w: p 329: odd, 73, 83, 91 – 95 odd.

Probability What Are the Chances?. Section 1 The Basics of Probability Theory Objectives: Be able to calculate probabilities by counting the outcomes.

Section 4.4 The Multiplication Rules & Conditional Probability

Probability Denoted by P(Event) This method for calculating probabilities is only appropriate when the outcomes of the sample space are equally likely.

Probability. Discussion Topics  Mutually exclusive events  Addition rule  Conditional probability  Independent event  Counting problem.

5.1 Introducing Probability Objectives: By the end of this section, I will be able to… 1) Understand the meaning of an experiment, an outcome, an event,

5.3 The Multiplication Rule

4-4 Multiplication Rules and Conditional Probability Objectives -understand the difference between independent and dependent events -know how to use multiplication.

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 13.1, Slide 1 13 Probability What Are the Chances?

Section 8.2: Expected Values

Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 13.1, Slide 1 13 Probability What Are the Chances?

“Baseball is 90% mental. The other half is physical.” Yogi Berra.

Lesson Conditional Probability and the General Multiplication Rule.

Section 4-3 The Addition Rule. COMPOUND EVENT A compound event is any event combining two or more simple events. NOTATION P(A or B) = P(in a single trial,

NOTES: Page 40. Probability Denoted by P(Event) This method for calculating probabilities is only appropriate when the outcomes of the sample space are.

Probability Denoted by P(Event) This method for calculating probabilities is only appropriate when the outcomes of the sample space are equally likely.

Lesson 6 - R Probability and Simulation: The Study of Randomness.

AP Statistics Exam Review

Probability Part2 ( ) Chapter 5 Probability Part2 ( )

Copyright © 2009 Pearson Education, Inc. Chapter 12 Section 1 - Slide 1 Unit 7 Probability.

III. Probability B. Discrete Probability Distributions

Topic 4A: Independent and Dependent Events Using the Product Rule

Chapter 4 Lecture 3 Sections: 4.4 – 4.5. Multiplication Rule Recall that we used addition for the P(A or B). the word “or” in P(A or B) suggests addition.

THE NATURE OF PROBABILITY Copyright © Cengage Learning. All rights reserved. 13.

Lesson 3-6. Independent Event – 1st outcome results of probability DOES NOT affect 2nd outcome results Dependent Event – 1st outcome results of probability.

Expected Value.

P(A). Ex 1 11 cards containing the letters of the word PROBABILITY is put in a box. A card is taken out at random. Find the probability that the card.

Lesson 6 – 3b General Probability Rules Taken from

Probability and Simulation Rules in Probability. Probability Rules 1. Any probability is a number between 0 and 1 0 ≤ P[A] ≤ 1 0 ≤ P[A] ≤ 1 2. The sum.

Chapter 6 Review Fr Chris Thiel 13 Dec 2004 What is true about probability? The probability of any event must be a number between 0 and 1 inclusive The.

Statistics General Probability Rules. Union The union of any collection of events is the event that at least one of the collection occurs The union of.

Section 3.2 Conditional Probability and the Multiplication Rule.

Exercises (1) 1. A man has two kids. What’s the probability that both are girls, given that one of them is a girl.

Slide Copyright © 2009 Pearson Education, Inc. Chapter 7 Probability.

Copyright © 2011 Pearson Education, Inc. Probability: Living with the Odds.

To find the probability of two events occurring together, you have to decide whether one even occurring affects the other event. * Dependent Events—the.

Examples 1.At City High School, 30% of students have part- time jobs and 25% of students are on the honor roll. What is the probability that a student.

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

Copyright © 2015, 2011, 2008 Pearson Education, Inc. Chapter 7, Unit B, Slide 1 Probability: Living With The Odds 7.

Section 5.3 Independence and the Multiplication Rule.

Middle Tennessee State University ©2013, MTStatPAL.

2.5 Additive Rules: Theorem 2.10: If A and B are any two events, then: P(A  B)= P(A) + P(B)  P(A  B) Corollary 1: If A and B are mutually exclusive.

A die is rolled. What is the probability that the number showing is odd? Select the correct answer

Warm Up What is the theoretical probability of rolling a die and landing on a composite number?

Monty Hall This is a old problem, but it illustrates the concept of conditional probability beautifully. References to this problem have been made in much.

Copyright © 2013, 2010 and 2007 Pearson Education, Inc. Chapter Probability 5.

PROBABILITY DISTRIBUTIONS. Probability Distribution  Suppose we toss a fair coin 3 times. What is the sample space?  What is the probability for each.

Probability Written as: P(Event)  Only appropriate if all outcomes are equally likely.

Thinking Mathematically Expected Value. Expected value is a mathematical way to use probabilities to determine what to expect in various situations over.

AP Statistics Probability Rules. Definitions Probability of an Outcome: A number that represents the likelihood of the occurrence of an outcome. Probability.

AP Statistics Chapter 6 Section 3. Review of Probability Rules 1.0 < P(A) < 1 2.P(S) = 1 3.Complement Rule: For any event A, 4.Addition Rule: If A and.

Probability. Definitions Probability: The chance of an event occurring. Probability Experiments: A process that leads to well- defined results called.

DO NOW 4/27/2016 Find the theoretical probability of each outcome. 1. rolling a 6 on a number cube. 2. rolling an odd number on a number cube. 3. flipping.

4.5 through 4.9 Probability continued…. Today’s Agenda Go over page 158 (49 – 52, 54 – 58 even) Go over 4.5 and 4.6 notes Class work: page 158 (53 – 57.

Probability Models Section 6.2.

Probability Rules.

Probability Rules and Models

Lecture Slides Elementary Statistics Eleventh Edition

Elementary Statistics

3 5 Chapter Probability © 2010 Pearson Prentice Hall. All rights reserved.

General Probability Rules

Week 7 Lecture 2 Chapter 13. Probability Rules.

Conditional Probability and the Multiplication Rule

Review: Mini-Quiz Combined Events

Chapter 4 Lecture 3 Sections: 4.4 – 4.5.

Presentation transcript:

Probability

Discussion Topics  Conditional Probability  Probability using the general multiplication rule  Independent event

Question 1 Males (In millions) Females (In millions) Totals (In millions) Never married Married Widowed Divorce Totals Calculate the probability that a randomly selected individual 18 years or older is widowed Calculate the probability that a randomly selected individual 18 years or older is widowed and female The data in the table below represent the marital status of males and females 18 years old or older

Solution Probability that selected individual is widowed: (a)Define W as the event of picking a widow P(W)=Total of widows/Overall totals F6/F8

Solution Probability that selected individual is widowed and female P(Widowed | Female)=Number of widowed/Number of females E6/E8

Question 2 In the game of roulette, the wheel has slots numbered 0,00, and 1 through 36.A metal ball is allowed to roll around a wheel until it falls into one of the numbered slots. You decide to play the game and place a bet on the number 17. (a) What is the probability that the ball will land in the slot numbered 17 two times in a row?

Solution The events are independent because the probability of the 1 st spin cannot affect the probability of the second spin. The ball does not remember it landed on 17 on the first spin (1/38)/(1/38)

Question 3 Suppose that a box of 100 circuits is sent to a manufacturing plant. Of the 100 circuits shipped, 5 are defective. The plant manager receiving the circuits randomly selects 2 and tests them. If both circuits work, she will accept the shipment. Otherwise the shipment is rejected. (a)Use a tree diagram to represent all possible outcomes (b) What is the probability that the plant manager discovers at least 1 defective circuit and rejects the shipment

Tree diagram Tool used is Microsoft Visio.

From our tree diagram and using addition rule: P(at least 1 defective) = P(GD) + P(DG) + P(DD) = = There is probability of shipment being rejected 2 nd Approach: P(at least 1 defective) = 1-P(none defective) = 1- (95/100)*(94/99) = = 0.098

CSTEM Web link  Presentation slides  Problems  Guidelines  Learning materials