(Ch5) Using the following contingency table, we can find P(A1 U B2) is A₁ Row Total 68 148 64 150 72 169 204 467 B₁ B₂ B3 Col Total Select one: a. 0.3182 O b. 0.3854 O C. O d. 0.0300 0.0933 A₁ 12 14 18 44 26 28 32 86 A3 42 44 47 133
(Ch5) Using the following contingency table, we can find P(A1 U B2) is A₁ Row Total 68 148 64 150 72 169 204 467 B₁ B₂ B3 Col Total Select one: a. 0.3182 O b. 0.3854 O C. O d. 0.0300 0.0933 A₁ 12 14 18 44 26 28 32 86 A3 42 44 47 133
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Chapter 5: Probability and Statistics**
In this section, we will explore how to calculate probabilities using a contingency table.
**Example Problem**
Given the following contingency table, we will find the probability \( P(A1 \cup B2) \).
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
& A_1 & A_2 & A_3 & A_4 & \text{Row Total} \\
\hline
B_1 & 12 & 26 & 42 & 68 & 148 \\
\hline
B_2 & 14 & 28 & 44 & 64 & 150 \\
\hline
B_3 & 18 & 32 & 47 & 72 & 169 \\
\hline
\text{Col Total} & 44 & 86 & 133 & 204 & 467 \\
\hline
\end{array}
\]
**Instructions**
To solve for \( P(A1 \cup B2) \), we consider the union of events \( A1 \) and \( B2 \). This includes all occurrences in row 2 and column 1 without double-counting.
- The total events in \( A1 \) is the sum of column A1: \( 44 \).
- The total events in \( B2 \) is the sum of row B2: \( 150 \).
The formula for probability of a union of two events in a contingency table is:
\[ P(A_1 \cup B_2) = \frac{\text{Total in } A_1 + \text{Total in } B_2 - \text{Intersection of } A_1 \text{ and } B_2}{\text{Total events}} \]
\[ = \frac{44 + 150 - 14}{467} = \frac{180}{467} \approx 0.3854 \]
**Select one:**
- a. 0.3182
- b. **0.3854**
- c. 0.0933
- d. 0.0300
**Explanation of Diagram**
The table shows combinations of events \( A1, A2, A3, A4 \) with \( B1, B2, B3 \). Each cell represents the count of occurrences](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5c9e71a-2152-46c3-8ddc-78ecbd167355%2F3e3001e7-0236-4348-8459-b68d29a015de%2Flbrpzxb_processed.png&w=3840&q=75)
Transcribed Image Text:**Chapter 5: Probability and Statistics**
In this section, we will explore how to calculate probabilities using a contingency table.
**Example Problem**
Given the following contingency table, we will find the probability \( P(A1 \cup B2) \).
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
& A_1 & A_2 & A_3 & A_4 & \text{Row Total} \\
\hline
B_1 & 12 & 26 & 42 & 68 & 148 \\
\hline
B_2 & 14 & 28 & 44 & 64 & 150 \\
\hline
B_3 & 18 & 32 & 47 & 72 & 169 \\
\hline
\text{Col Total} & 44 & 86 & 133 & 204 & 467 \\
\hline
\end{array}
\]
**Instructions**
To solve for \( P(A1 \cup B2) \), we consider the union of events \( A1 \) and \( B2 \). This includes all occurrences in row 2 and column 1 without double-counting.
- The total events in \( A1 \) is the sum of column A1: \( 44 \).
- The total events in \( B2 \) is the sum of row B2: \( 150 \).
The formula for probability of a union of two events in a contingency table is:
\[ P(A_1 \cup B_2) = \frac{\text{Total in } A_1 + \text{Total in } B_2 - \text{Intersection of } A_1 \text{ and } B_2}{\text{Total events}} \]
\[ = \frac{44 + 150 - 14}{467} = \frac{180}{467} \approx 0.3854 \]
**Select one:**
- a. 0.3182
- b. **0.3854**
- c. 0.0933
- d. 0.0300
**Explanation of Diagram**
The table shows combinations of events \( A1, A2, A3, A4 \) with \( B1, B2, B3 \). Each cell represents the count of occurrences
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 7 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman