ES Lec. 5
Page 1: Course Introduction
Course Offered: Engineering Statistics
Instructor: Dr. Mohamad Kharseh
Office: G 342
Email: mohamad.kharseh@aurak.ac.ae
Page 2: Course Feedback Survey
Students will have the opportunity to provide feedback at the end of each lecture.
Page 3: Lecture Overview
Lecture 5: Visualizing Events
Page 4: Fundamental Probability
Formula: P(A) = P(A and B1) + P(A and B2) + … + P(A and Bk)
B1, B2, …, Bk are possible outcomes.
Example: Tossing a fair coin twice to find the probability of observing at least one head:
Possible outcomes: 1/4 (TT), 1/4 (TH), 1/4 (HT), 1/4 (HH)
Calculation: P(at least 1 head) = P(TH) + P(HT) + P(HH) = 3/4
Page 5: Marginal Probability
Example: Probability of drawing an Ace from a deck of 52 cards:
P(Ace) = P(Ace and Red) + P(Ace and Black) = 2/52 + 2/52 = 4/52.
Page 6: Visualizing Events
Overview of visual tools for understanding probability events.
Page 7: Contingency Tables
Definition: A statistical table showing the distribution of two or more categorical variables.
Structure: Organized into rows and columns with frequencies or counts.
Page 8: Marginal Probability Using Contingency Table
Example representation:
Ace-Color breakdown:
Red Aces: 2
Black Aces: 2
Non-Aces: 48
Total: 52 cards
Page 9: Joint Probability Example
Calculation: P(Red and Ace) = (Number of Red Aces) / (Total Cards) = 2/52.
Page 10: Joint & Marginal Probabilities in Contingency Table
Variables studied with respective categories.
Page 11: Venn Diagrams
Definition: Graphical representations that show relationships between sets.
Example: Rolling a die and relating events of getting an even number versus an odd number.
Page 12: Venn Diagram Definition Example
Example: Among 25 students: 16 in Course A, 9 in Course B, 4 in both.
Page 13: Mutually Exclusive Events
Definition: Two events that cannot happen at the same time.
Illustrated using Venn diagrams, showing overlaps versus exclusivity.
Page 14: Calculating Probability with Venn Diagram
Non-mutually exclusive events: Probability calculated by understanding overlap.
Page 15: Addition Rule
Rule application for mutually exclusive events:
If mutually exclusive: P(A or B) = P(A) + P(B).
For non-mutually exclusive: P( A or B ) = P(A) + P(B) - P(A ∩ B).
Page 16: Example Application
Case of selecting a Jack or a heart from cards, demonstrating non-mutual exclusivity.
Page 17: Event Representation in Venn Diagram
Visual representation of selecting a Jack or heart.
Page 18: Example of Course Failures
Event probabilities related to students failing Statistics and Computer Application:
P(A U B) = P(A) + P(B) - P(A and B).
Page 19: Rolling a Die Example
Finding probabilities of rolling values less than 3 or exactly 4s, exploring mutual exclusivity.
Page 20: Solution to Die Rolling Example
Events are mutually exclusive, and probability calculations are made accordingly.
Page 21: General Addition Rule Example
Application of general probability principles, ensuring no double counting of events.
Page 22: Decision Trees
Definition: Tree-like structures representing outcomes of experiments.
Page 23: Coin Toss Example
Probability calculations based on multiple tosses of a fair coin.
Page 24: Selecting M&M Example
Assessing probabilities regarding red M&M selections using conditional probabilities.
Page 25: Tree Diagram Scenario
Using a tree diagram to work through possible gender combinations of three children.
Page 26: Gender Probability Solutions
Outcomes analyzed for probabilities of genders in childbirth scenarios.
Page 27: In-Class Assignment 1
Scenarios based on employee benefits, leading to various probability calculations.
Page 28: Solutions for Probability Assignment
Filling in Venn diagrams and determining probabilities based on employees' benefits.
Page 29: In-Class Assignment 2
Class assignment to calculate probabilities on students' study hours.
Page 30: Solution Approaches for Study Hours
Mutual exclusivity considered in assignment calculations.
Page 31: In-Class Assignment 3
Assignment involving Biology and Math enrollment.
Page 32: Biology Probability Calculation
Ratio computations for class enrollment situations based on provided scenarios.
Page 33: Thank You
Closure for the course outline or context.