Multiplication Rules for Probability Independent Events Two events are independent if the fact that A occurs does not affect the probability of B occuring.

Slides:



Advertisements
Similar presentations
Probability and Counting Rules
Advertisements

Conditional Probability and the Multiplication Rule
AP Statistics Section 6.2C Independent Events & The Multiplication Rule.
Multiplication Rule: Basics
Section 4.4 The Multiplication Rules & Conditional Probability
Probability Rules Section 4.2 Created by Laura Ralston.
MAT 103 Probability In this chapter, we will study the topic of probability which is used in many different areas including insurance, science, marketing,
Probability Sample Space Diagrams.
Chapter 4 Using Probability and Probability Distributions
4-4 Multiplication Rules and Conditional Probability Objectives -understand the difference between independent and dependent events -know how to use multiplication.
3.2 Conditional Probability & the Multiplication Rule Statistics Mrs. Spitz Fall 2008.
Section 4.3 The Addition Rules for Probability
Chapter 6 Probabilit y Vocabulary Probability – the proportion of times the outcome would occur in a very long series of repetitions (likelihood of an.
 Probability- the likelihood that an event will have a particular result; the ratio of the number of desired outcomes to the total possible outcomes.
Conditional Probability
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.
Dependent and Independent Events. Events are said to be independent if the occurrence of one event has no effect on the occurrence of another. For example,
Conditional Probability CHAPTER 4.3. INTRO TO VENN DIAGRAMS - PETS.
Sec 4.4 The multiplication Rule and conditional probability.
Chapter 4.3 Multiplication Rules.
Probability Probability is the measure of how likely an event is. An event is one or more outcomes of an experiment. An outcome is the result of a single.
Chapter 12 – Probability and Statistics 12.4 – Multiplying Probabilities.
Conditional Probability and the Multiplication Rule
7th Probability You can do this! .
Copyright © 2011 Pearson Education, Inc. Probability: Living with the Odds Discussion Paragraph 7A 1 web 70. Blood Groups 71. Accidents 1 world 72. Probability.
Section 3.2 Notes Conditional Probability. Conditional probability is the probability of an event occurring, given that another event has already occurred.
DEFINITION  INDEPENDENT EVENTS:  Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.
Copyright © 2015, 2012, and 2009 Pearson Education, Inc. 1 Chapter Probability 3.
Section 3.2 Conditional Probability and the Multiplication Rule.
Conditional Probability and the Multiplication Rule.
Section 3.2 Conditional Probability and the Multiplication Rule.
Probability What’s the chance of that happening? MM1D2 a, b, c.
MULTIPLICATION RULES FOR PROBABILITY INDEPENDENT AND DEPENDENT EVENTS.
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.
9-7Independent and Dependent Events 9-7 Independent and Dependent Events (pg ) Indicator: D7.
Chapter 10 – Data Analysis and Probability 10.8 – Probability of Independent and Dependent Events.
Independent Events The occurrence (or non- occurrence) of one event does not change the probability that the other event will occur.
Conditional Probability and the Multiplication Rule NOTES Coach Bridges.
Copyright © 2011 Pearson Education, Inc. Probability: Living with the Odds.
Independent and Dependent Events Lesson 6.6. Getting Started… You roll one die and then flip one coin. What is the probability of : P(3, tails) = 2. P(less.
Aim: How do we find the conditional probability of an event? TEST TUESDAY.
3.2-Conditional Probability The probability of an event occurring given another event has already occurred. P(B|A) = “Probability of B, given A” # outcomes.
Section 3.2 Conditional Probability and the Multiplication Rule Larson/Farber 4th ed 1.
Chance We will base on the frequency theory to study chances (or probability).
Probability. Definitions Probability: The chance of an event occurring. Probability Experiments: A process that leads to well- defined results called.
Probability What is the probability of rolling “snake eyes” in one roll? What is the probability of rolling “yahtzee” in one roll?
§12.4 Multiplying Probabilities Algebra II Honors.
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.
Section 3.2 Conditional Probability and the Multiplication Rule © 2012 Pearson Education, Inc. All rights reserved. 1 of 88.
Conditional Probability 423/what-is-your-favorite-data-analysis-cartoon 1.
Independence and Conditional Probability
4-3 The Multiplication Rules Conditional Probability
Chapter 3 Probability.
Conditional Probability and the Multiplication Rule
Conditional Probability & the Multiplication Rule
Aim: What is the multiplication rule?
4-4 The Multiplication Rules and Conditional Probability
Multiplication Rule and Conditional Probability
Test 4-5 is tentatively scheduled for Tuesday Oct 28
Elementary Statistics: Picturing The World
Probability and Statistics Chapter 3 Notes
Chapter 3 Probability.
Chapter 3 Probability Larson/Farber 4th ed.
Probability of TWO EVENTS
Conditional Probability
Investigation Write down the sample space for throwing a die and tossing a coin. 1T 2T 3T 4T 5T 6T 1H 2H 3H 4H 5H 6H   From the sample space calculate:
Presentation transcript:

Multiplication Rules for Probability Independent Events Two events are independent if the fact that A occurs does not affect the probability of B occuring.  Flip a coin 5 times…  drawing a card, replacing it, drawing again

Multiplication Rules for Probability Multiplication Rule 1 When two events are independent, the probability of both occuring is P(A and B) = P(A)P(B)  A coin is flipped and a die is rolled. Find the probability of getting a head on the coin and a 4 on the die.  A card is drawn and replaced. Find the probability of drawing a queen and then an ace.  The multiplication rule can be extended to many events…

Multiplication Rules for Probability Multiplication Rule 2 when two events are dependent, the probability of both occurring is P(A and B) = P(A)·P(B|A)  P(B|A) is a conditional probability  It means the probability that B occurs given that A has already occurred.

Multiplication Rules for Probability examples  A person owns 30 CD’s. 5 of them are jazz. If 2 CD’s are selected at random, what is the probability that both are jazz music? Are the two selections independent?  P(J 1 and J 2 ) =  53% of residents of a city have homeowner’s insurance. Of these 27% also have car insurance. Find P(home ins. and car ins.).

Multiplication Rules for Probability  try p 220 # 1 in your notes

Multiplication Rules for Probability Conditional Probability The probability that the second event B occurs given that the first event A has occurred is found by: P(B|A) = P(A and B) P(A)

Example  P(B and W) is 15/56 and P(B) 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.

 The probability that Sam parks in a no- parking zone and gets a ticket is 0.06 and the probability that Sam cannot find a 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- parking zone. Find the probability that he will get a ticket.

“At- least”  A game is played by drawing 4 cards from an ordinary deck and replacing each card after it is drawn. Find the probability that at least 1 ace is drawn. It is easier to find the probability that no aces are drawn and subtract that answer from 1.

A coin is tossed 5 times. Find the probability of getting at least 1 tail.

Multiplication Rules for Probability turn to page 221  try number 11 in your notes  try number 13

Practice  In class p 220 (2-30 even)