Sec 4.4 The multiplication Rule and conditional probability.

Slides:



Advertisements
Similar presentations
Probability and Counting Rules
Advertisements

5-1 Chapter 5 Probability 1.
AP Statistics Section 6.2C Independent Events & The Multiplication Rule.
Section 4.4 The Multiplication Rules & Conditional Probability
Probability Rules Section 4.2 Created by Laura Ralston.
Describing Probability
Probability Sample Space Diagrams.
Multiplication Rules for Probability Independent Events Two events are independent if the fact that A occurs does not affect the probability of B occuring.
4-4 Multiplication Rules and Conditional Probability Objectives -understand the difference between independent and dependent events -know how to use multiplication.
Section 4.3 The Addition Rules for Probability
 Probability- the likelihood that an event will have a particular result; the ratio of the number of desired outcomes to the total possible outcomes.
Lesson 18b – Do Now Do now Expectations: No talking for any reason, please. 1) A tube of sweets contains 10 red sweets, 7 blue sweets, 8 green sweets and.
Probability and Counting Rules
Gender Ratio CIA Fact Book. Sec 4.3  Addition Rules for Probability.
Conditional Probability
“PROBABILITY” Some important terms Event: An event is one or more of the possible outcomes of an activity. When we toss a coin there are two possibilities,
Compound Probability Pre-AP Geometry. Compound Events are made up of two or more simple events. I. Compound Events may be: A) Independent events - when.
Copyright © Ed2Net Learning Inc.1. 2 Warm Up Use the Counting principle to find the total number of outcomes in each situation 1. Choosing a car from.
Chapter 1:Independent and Dependent Events
COUNTING RULES PROBLEMS 1. How many different ways can a nurse visit 9 patients if she wants to visit them all in one day? If she wants to visit only 5?
Conditional Probability CHAPTER 4.3. INTRO TO VENN DIAGRAMS - PETS.
Chapter 4.3 Multiplication Rules.
Topic 4A: Independent and Dependent Events Using the Product Rule
Warm Up 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 two coins.
Chapter 12 – Probability and Statistics 12.4 – Multiplying Probabilities.
Sec 4.4 Counting Rules Bluman, Chapter 4 A Question to Ponder:  A box contains 3 red chips, 2 blue chips and 5 green chips. A chip is selected, replaced.
7th Probability You can do this! .
Algebra II 10.4: Find Probabilities of Disjoint and Overlapping Events HW: HW: p.710 (8 – 38 even) Chapter 10 Test: Thursday.
Warm Up a) 28 b) ½ c) Varies Packet signatures???.
Probability What’s the chance of that happening? MM1D2 a, b, c.
Probability of Multiple Events.  A marble is picked at random from a bag. Without putting the marble back, a second one has chosen. How does this affect.
1 Chapter 3. Section 3-4. Triola, Elementary Statistics, Eighth Edition. Copyright Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.
Probability.
Math 30-2 Probability & Odds. Acceptable Standards (50-79%)  The student can express odds for or odds against as a probability determine the probability.
Independent Events Lesson Starter State in writing whether each of these pairs of events are disjoint. Justify your answer. If the events.
Do Now. Introduction to Probability Objective: find the probability of an event Homework: Probability Worksheet.
Unit 4 Section : Conditional Probability and the Multiplication Rule  Conditional Probability (of event B) – probability that event B occurs.
Chapter 10 – Data Analysis and Probability 10.8 – Probability of Independent and Dependent Events.
Conditional Probability and the Multiplication Rule NOTES Coach Bridges.
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.
13-4 Probability of Compound Events. Probability of two independent events A and B. P(A and B)=P(A)*P(B) 1)Using a standard deck of playing cards, find.
Copyright © 2015, 2011, 2008 Pearson Education, Inc. Chapter 7, Unit B, Slide 1 Probability: Living With The Odds 7.
Aim: How do we find the conditional probability of an event? TEST TUESDAY.
11.3 Probability of Multiple Events Learning goal find the probability of the event A and B find the probability of the event A or B.
Chance We will base on the frequency theory to study chances (or probability).
Addition Rules for Probability.  Two events are mutually exclusive events if they cannot occur at the same time (i.e., they have no outcomes in common)
Question 1 Q. Four cards are drawn from a pack of 52 cards. Find the probability of, 1. They are King, Queen, Jack, & Ace 2. First is King, then Queen,
Sample Spaces and Probability Addition Rules Multiplication Rules and Conditional Probability Counting Rules Probability and Counting Rules
Probability. Definitions Probability: The chance of an event occurring. Probability Experiments: A process that leads to well- defined results called.
Warm-Up #9 (Tuesday, 2/23/2016) 1.(Use the table on the left) How many students are in the class? What fraction of the students chose a red card? ResultFrequency.
Note: This PowerPoint is only a summary and your main source should be the book. 4-2 Addition Rules for Probability Instructor: Alaa saud CHAPTER 4.
Independence and Conditional Probability
4-3 The Multiplication Rules Conditional Probability
Probability of Independent and Dependent Events
Aim: What is the multiplication rule?
4-4 The Multiplication Rules and Conditional Probability
What Is Probability?.
Multiplication Rule and Conditional Probability
4-4 Multiplication Rules.
Combining Probabilities
Test 4-5 is tentatively scheduled for Tuesday Oct 28
Probability of Independent and Dependent Events
Probability of Independent and Dependent Events
Probability of Independent and Dependent Events
Probability: Living with the Odds
Section 12.2 Theoretical Probability
Conditional Probability and the Multiplication Rule
Probability of Dependent and Independent Events
Probability of Independent and Dependent Events
Presentation transcript:

Sec 4.4 The multiplication Rule and conditional probability

Independent events  Two events A and B are independent events if the fact that A occurs does NOT effect the probability of B occurring.

Multiplication Rule 1  If two events are independent, the probability of both happening is  P(A and B)= P(A) P(B)

Examples  A coin is flipped and a die is rolled at the same time. What is the probability of getting a tail and a 4?  A card is drawn at random and then replaced. What is the probability of drawing a queen first and then an ace?

More examples  A box contains 3 red balls, 2 blue balls and 5 green balls. A ball is selected, replaced and a second ball is selected. Write the sample space. Write the probability of each event.

Refer to the last example and answer the following probabilities: a)Selecting 2 blue balls. b)Selecting 1 blue ball and then 1 green ball. c)Selecting 1 red ball and then 1 blue.

Color blindness  Studies show that approximately 9% of men have color blindness. If 3 males are selected at random what is the probability that none of them have color blindness?

Refer to the color blindness problem  If 3 men are chosen at random. What is the sample space for color blindness?  Do you think each event has the same probability of happening?

Dependent events  When the outcome of the first event affects the outcome of the second event in such a way that the probability is changed, the events are dependent.

Multiplication Rule #2  When two events are dependent, the probability of both happening is  P(A and B)= P(A) · P(B|A)

Example 4-28  A person owns a collection of 30 CDs, of which 5 are country music. If 2 CDs are selected at random, find the probability that both are country music.

Example 4-29  The World Wide Insurance Company found that 53% of the residents of a city had homeowner’s insurance (H) with the company. Of these clients, 27% also had automobile insurance (A) with the company. If a resident is selected at random, find the probability that the resident has both homeowner’s and automobile insurance with the World Wide Insurance Company.

Example 4-30  Three cards are drawn from an ordinary deck and not replaced. Find the probability of these.  A.) Getting 3 jacks.  B.) Getting an ace, a king, and a queen in order.  C.) Getting a club, a spade, and a heart in order.  D.) Getting 3 clubs.

Example 4-31  Box 1 contains 2 red balls and 1 blue ball. Box 2 contains 3 blue balls and 1 red ball. A coin is tossed. If it falls heads up, box 1 is selected and a ball is drawn. If it falls tails up, box 2 is selected and a ball is drawn. Find the probability of selecting a red ball.

Formula for Conditional Probability  The probability that the second event B occurs given that the first event A has occurred can be found by dividing the probability that both events occurred by the probability that the first event has occurred. The formula is:

Example 4-32  A box contains black chips and white chips. A person selects two chips without replacement. If the probability of selecting a black chip and a white chip is 15/56, and the probability of selecting a black chip on the first draw is 3/8, find the probability of selecting the white chip on the second draw, given that the first chip selected was a black chip.

Example 4-33  The probability that Sam parks in a no- parking zone and gets a parking ticket is 0.06, and the probability that Sam cannot find a legal parking space and has to park in the no-parking zone is On Tuesday, Sam arrives at school and has to park in a no- park zone. Find the probability that he will get a parking ticket.

Example 4-34  A recent survey asked 100 people if they thought women in the armed forces should be permitted to participate in combat. The results of the survey are shown.  Male Yes-32, No-18 Total-50  Female Yes-8 No-42 Total-50  Find these probabilities.  A.) The respondent answered yes, given that the respondent was a female.  B.) The respondent was a male, given that the respondent answered no.

Probabilities for “At Least”  The multiplication rules can be used with the complementary event rule (Section 4-2) to simplify solving probability problems involving “at least.” Examples 4-35, 4-36, and 4-37 illustrate how this is done.

Example 4-35  A game is played by drawing four cards from an ordinary deck and replacing each card after it is drawn. Find the probability of winning if at least one ace is drawn.

Example 4-36  A coin is tossed 5 times. Find the probability of getting at least one tail.

Example 4-37  The Newckware Association of America reported that 3% of ties sold in the United States are bow ties. If 4 customers who purchased a tie are randomly selected, find the probability that at least one purchased a bow tie.

Homework  Sec 4.4 page  #1-51 Every other odds. i.e 1,5,9, etc.