Probability COMPOUND EVENTS. If two sets or events have no elements in common, they are called disjoint or mutually exclusive. Examples of mutually exclusive.

Slides:

Advertisements

Similar presentations

Probability of Independent Events

Advertisements

Beginning Probability

WARM UP Students that were here last class, get with your groups and finish your Mutually Exclusive problems New students wait until attendance is called.

MAT 103 Probability In this chapter, we will study the topic of probability which is used in many different areas including insurance, science, marketing,

Unions and Intersections  When you consider all the outcomes for either of two events, A and B, you form the union of A and B.  When you consider only.

Probability of Compound Events

12- 8 Probability of Compound Events

Lecture 13 Elements of Probability CSCI – 1900 Mathematics for Computer Science Fall 2014 Bill Pine.

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

Rare Events, Probability and Sample Size. Rare Events An event E is rare if its probability is very small, that is, if Pr{E} ≈ 0. Rare events require.

EQ: What are compound events?

Copyright © Cengage Learning. All rights reserved. 8.6 Probability.

8.7 Probability. Ex 1 Find the sample space for each of the following. One coin is tossed. Two coins are tossed. Three coins are tossed.

Chapter 10.4B More with OR Probability.

Find Probabilities of Disjoint and Overlapping Events

13-4 Compound Probability

The Addition Rule and Complements 5.2. ● Venn Diagrams provide a useful way to visualize probabilities  The entire rectangle represents the sample space.

Section 5.2 The Addition Rule and Complements

EXAMPLE 1 Find probability of disjoint events

12.4 Probability of Compound Events

Section 2 Probability Rules – Compound Events Compound Event – an event that is expressed in terms of, or as a combination of, other events Events A.

Copyright © Cengage Learning. All rights reserved. Elementary Probability Theory 5.

Special Topics. General Addition Rule Last time, we learned the Addition Rule for Mutually Exclusive events (Disjoint Events). This was: P(A or B) = P(A)

Chapter 7: Probability Lesson 2: Addition Counting Principles Mrs. Parziale.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 12.6 OR and AND Problems.

Chapter 1:Independent and Dependent Events

Copyright © Cengage Learning. All rights reserved. 8.6 Probability.

Algebra II 10.4: Find Probabilities of Disjoint and Overlapping Events HW: HW: p.710 (8 – 38 even) Chapter 10 Test: Thursday.

Chapter 4 Probability. Definitions A probability experiment is a chance process that leads to well-defined results called outcomes. An outcome is the.

12.4 Probability of Compound Events. Vocabulary Compound Event: the union or intersection of two events. Mutually Exclusive Events: events A and B are.

Probability Rules In the following sections, we will transition from looking at the probability of one event to the probability of multiple events (compound.

EXAMPLE 1 Find probability of disjoint events A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a 10 or.

Mutually Exclusive Events. In some situations, more than one event could occur during a single trial. In some situations, more than one event could occur.

Warm-up 1)You roll a number cube once. Then roll it again. What is the probability that you get 2 on the first roll and a number greater than 4 on the.

Introduction Remember that probability is a number from 0 to 1 inclusive or a percent from 0% to 100% inclusive that indicates how likely an event is to.

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

Single Pick Probability AND vs. OR Sequential Probability With Replacement Conditional Disjoint vs. Non Disjoint Unit 4 – Probability – Part 1.

I can find probabilities of compound events.. Compound Events  Involves two or more things happening at once.  Uses the words “and” & “or”

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.

Probability How likely it is that something will happen.

Probability What is the probability of rolling “snake eyes” in one roll? What is the probability of rolling “yahtzee” in one roll?

16.6 Expected Value.

Conditional Probability 423/what-is-your-favorite-data-analysis-cartoon 1.

Adding Probabilities 12-5

Lesson 10.4 Probability of Disjoint and Overlapping Events

What Is Probability?.

10.7: Probability of Compound Events Test : Thursday, 1/16

4 Elementary Probability Theory

Bellwork Perform Synthetic Division and explain what is the solution of the synthetic division represent?

Section 12.2 Probability.

9.7 Probability of Compound Events

12.4 Probability of Compound Events

4 Elementary Probability Theory

Introduction Remember that probability is a number from 0 to 1 inclusive or a percent from 0% to 100% inclusive that indicates how likely an event is to.

5 Elementary Probability Theory

A card is drawn from a standard deck of 52 cards.

A simple event is an event that describes a single outcome

Compound Probability.

SECTION 4.3 ADDITION RULE 1.

Mutually Exclusive Events

Probability General Addition Rule Multiplication Rule

12.4 Find Probabilities of Disjoint and Overlapping Events

Find Probabilities of Disjoint and Overlapping Events

Probability with more than 1 event

Section 12.6 OR and AND Problems

Unit 6: Application of Probability

Adapted from Walch Education

What is the 5th term in the expansion of (2a + b)6?

A random experiment gives rise to possible outcomes, but any particular outcome is uncertain – “random”. For example, tossing a coin… we know H or T will.

Presentation transcript:

Probability COMPOUND EVENTS

If two sets or events have no elements in common, they are called disjoint or mutually exclusive. Examples of mutually exclusive sets: Two fair dice are tossed, what is the probability of a sum of 7 or 11? A card is randomly selected from a standard deck of cards. What is the probability that it is a 10 OR a face card? If A and B are disjoint events, then the probability of A OR B is: P( A or B) = P(A ) + P(B)

Examples of mutually exclusive sets: Two fair dice are tossed, what is the probability of a sum of 7 or 11?

Examples of mutually exclusive sets: A card is randomly selected from a standard deck of cards. What is the probability that it is a 10 OR a face card?

Examples of mutually exclusive sets: In this last situation there is no overlap: 10

But if I changed the question to: A card is randomly selected from a standard deck of cards. What is the probability that it is a 10 OR a heart?

So we need to modify our formula and subtract out that overlap so we don’t count it twice: This is called a COMPOUND EVENT.

Two sets are INDEPENDENT if the occurrence of one has NO EFFECT on the occurrence of the other. Examples of independent: Two fair dice are tossed, what is the probability of a sum of 12? A computer generates three random numbers…. P( A and B) = P(A ) ∙ P(B) NOTICE: There is no “ or”. Compound events ask for probability of this “ or” that. If there is overlap we are also able to find a this “and” that”.

Out of 200 students 113 are either varsity athletes or on the honor roll. There are 74 students who are varsity athletes and 51 who are on the honor roll. What is the probability that a randomly selected senior is both a varsity athlete AND on the honor roll?