Management Science BUS 340

Slides:

Advertisements

Similar presentations

Section Independent Events

Advertisements

Disjointed and Overlapping Event Disjointed events (mutually exclusive) - are events that have no outcome in common Overlapping events- events that have.

The Practice of Statistics Third Edition Chapter 6: Probability and Simulation: The Study of Randomness Copyright © 2008 by W. H. Freeman & Company Daniel.

Problem Northside Rifle Team

Review For Probability Test

Chapter 12: Conditional Probability & Independence 1.(12.1) Conditional Probability 2.(12.2) Independence 1.(12.1) Conditional Probability 2.(12.2) Independence.

EXAMPLE 1 Standardized Test Practice SOLUTION Let events A and B be getting the winning ticket for the gift certificate and movie passes, respectively.

Chapter Two Probability. Probability Definitions Experiment: Process that generates observations. Sample Space: Set of all possible outcomes of an experiment.

P robability Sample Space 郭俊利 2009/02/27. Probability 2 Outline Sample space Probability axioms Conditional probability Independence 1.1 ~ 1.5.

Learning Goal 13: Probability Use the basic laws of probability by finding the probabilities of mutually exclusive events. Find the probabilities of dependent.

Probability Rules l Rule 1. The probability of any event (A) is a number between zero and one. 0 < P(A) < 1.

The Erik Jonsson School of Engineering and Computer Science Chapter 1 pp William J. Pervin The University of Texas at Dallas Richardson, Texas

Chapter 8 Probability Section R Review. 2 Barnett/Ziegler/Byleen Finite Mathematics 12e Review for Chapter 8 Important Terms, Symbols, Concepts  8.1.

Probability of Compound Events

Section 1.6 Suppose that S = B 1  B 2  …  B m is an outcome space with B i  B j =  for i  j, that is, B 1, B 2, …, B m are mutually exclusive and.

Tree Diagram Worksheet

Chapter 12 Probability. Chapter 12 The probability of an occurrence is written as P(A) and is equal to.

Geometric and Binomial Models (part un) AP Statistics Chapter 17.

Conditional Probability Objective: I can find the probability of a conditional event.

Probability Definition: Probability: the chance an event will happen. # of ways a certain event can occur # of possible events Probability =  Probability.

Recap from last lesson Compliment Addition rule for probabilities

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

Two-Way Tables General Addition Rule Aim: Create & use two-way tables to find probabilities involving ‘or’.

12/7/20151 Math b Conditional Probability, Independency, Bayes Theorem.

Chapter 4 (continued) Nutan S. Mishra Department of Mathematics and Statistics University of South Alabama.

Probability Rules. We start with four basic rules of probability. They are simple, but you must know them. Rule 1: All probabilities are numbers between.

Probability. Rules  0 ≤ P(A) ≤ 1 for any event A.  P(S) = 1  Complement: P(A c ) = 1 – P(A)  Addition: If A and B are disjoint events, P(A or B) =

In-Class Exercises: Axioms of Probability

Let A and B be two independent events for which P(A) = 0.15 and P(B) = 0.3. Find P(A and B).

9-7Independent and Dependent Events 9-7 Independent and Dependent Events (pg ) Indicator: D7.

Independent Events The occurrence (or non- occurrence) of one event does not change the probability that the other event will occur.

Starter P(A) = ½, P(B) = ⅓ and P(A B) = p Find p if:

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

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

P(B) = Triangle Area P(A) = Oval Area P(A or B) = r + w + g P(A and B) = w So, P(A) + P(B) = r + w + g + w The Addition Rule for 2 events A and B P(A or.

STATISTICS 6.0 Conditional Probabilities “Conditional Probabilities”

MAT 142 Lecture Video Series. Combinatorics and Probability.

Conditional Probability If two events are not mutually exclusive, the fact that we know that B has happened will have an effect on the probability of A.

Microsoft produces a New operating system on a disk. There is 0

Review Conditional Probability –Denoted P(A|B), it represents the probability that A will occur given that B occurred. Independent events –Two events A.

Chapter 15: Probability Rules! Ryan Vu and Erick Li Period 2.

When a normal, unbiased, 6-sided die is thrown, the numbers 1 to 6 are possible. These are the ONLY ‘events’ possible. This means these are EXHAUSTIVE.

Probability Assignment #41 Review Paper #1 day7. Probability A#41 Review Paper #1 day7.

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 9-7 Probability of Multiple Events. Multiple Events When the occurrence of one event affects the probability of a second event the two events.

Chapter 3 Probability.

Chapter 3 Probability.

Statistics 300: Introduction to Probability and Statistics

12.4 Probability of Compound Events

AP Statistics Chapter 6 Review

MATH 2311 Section 2.4.

Conditional Probability AGENDA

Have Fridays homework out

I can find probabilities of compound events.

Mutually exclusive nothing in common.

Introduction to Probability & Statistics Expectations

Mutually Exclusive Events

Section 11.7 Probability.

Chapter 4 Probability 4.2 Basic Concepts of Probability

MATH 2311 Section 2.4.

General Probability Rules

Probability Rules Rule 1.

Note 9: Laws of Probability

Probability Mutually exclusive and exhaustive events

Notes 13-4: Probabilities of Compound Events

Chapter 3 Probability.

Chapter 3 Probability.

Presentation transcript:

Management Science BUS 340 Chapter 2 Problem 2-24 Presented by: Kelly Devilbiss

Boston South Fifth Street Softball League Win-Loss Record (past 5 years) Winner (1) (2) (3) Mama’s Boys (1) X 3 4 The Killers (2) 2 1 The Machos (3) Kelly Devilbiss

a. What is the probability that the Killers will win every game next year? Solution: Joint Probability: P(AB) = P(A) x P(B) P(Killers beating the Mama’s Boys) = 2/5 In the last five years, the Killers have beat the Mama’s Boys 2 times. P(Killers beating the Machos) = 1/5 Machos 1 time. Kelly Devilbiss

b. What is the probability that the Machos will win at least one game next year? Solution: Law of Addition for events that are not mutually exclusive [P(A or B) = P(A) + P(B) – P(A and B)] P(Machos will beat the Mama’s Boys or the Killers) = ½ + ½ = .5 + .5 = 1.0 P(Machos will beat the Mama’s Boys and the Killers) = 1/5 x 4/5 = .2 x .8 = .16 Kelly Devilbiss

c. What is the probability that the Mama’s Boys will win exactly one game next year? Solution: Joint Probability for Independent Events P(AB) = P(A) x P(B) P(Mama’s Boys will win against the Killers) = 4/6 but P(Mama’s Boys will not win against the Machos) = 4/6 Kelly Devilbiss

d. What is the probability that the Killers will win less than two games next year? Solution: Law of Addition for events that are not mutually exclusive [P(A or B) = P(A) + P(B) – P(A and B)] P(Killers will against the Mama’s Boys or the Machos) = ½ + ½ = .5 + .5 = 1.0 P(Killers wins against the Mama’s Boys and the Machos) = 2/5 x 1/5 = .4 x .2 = .08 Kelly Devilbiss