U and V are mutually exclusive events. P(U) = 0.26; P(V) = 0.37. Find: a. P(UnV) b. P(U\V) PILLY)
U and V are mutually exclusive events. P(U) = 0.26; P(V) = 0.37. Find: a. P(UnV) b. P(U\V) PILLY)
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
![## Problem: Mutually Exclusive Events
Given:
- Events \( U \) and \( V \) are mutually exclusive.
- \( P(U) = 0.26 \)
- \( P(V) = 0.37 \)
Find the following probabilities:
### a. \( P(U \cap V) \)
### b. \( P(U \cup V) \)
### c. \( P(U | V) \)
**Solution:**
**a. Finding \( P(U \cap V) \)**
Since \( U \) and \( V \) are mutually exclusive, their intersection is empty. Therefore,
\[ P(U \cap V) = 0 \]
**b. Finding \( P(U \cup V) \)**
The Union of \( U \) and \( V \) for mutually exclusive events:
\[ P(U \cup V) = P(U) + P(V) \]
\[ P(U \cup V) = 0.26 + 0.37 \]
\[ P(U \cup V) = 0.63 \]
**c. Finding \( P(U | V) \)**
For mutually exclusive events, the conditional probability \( P(U | V) \) is given by:
\[ P(U | V) = \frac{P(U \cap V)}{P(V)} \]
Since \( P(U \cap V) = 0 \) (from part a),
\[ P(U | V) = \frac{0}{0.37} = 0 \]
So, the answers are:
- \( P(U \cap V) = 0 \)
- \( P(U \cup V) = 0.63 \)
- \( P(U | V) = 0 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faed2933e-b67f-42a0-9fac-b6dce0e828b0%2F944e7068-b64c-48fc-a9a3-c6886187d5d3%2Fvk9zw8d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem: Mutually Exclusive Events
Given:
- Events \( U \) and \( V \) are mutually exclusive.
- \( P(U) = 0.26 \)
- \( P(V) = 0.37 \)
Find the following probabilities:
### a. \( P(U \cap V) \)
### b. \( P(U \cup V) \)
### c. \( P(U | V) \)
**Solution:**
**a. Finding \( P(U \cap V) \)**
Since \( U \) and \( V \) are mutually exclusive, their intersection is empty. Therefore,
\[ P(U \cap V) = 0 \]
**b. Finding \( P(U \cup V) \)**
The Union of \( U \) and \( V \) for mutually exclusive events:
\[ P(U \cup V) = P(U) + P(V) \]
\[ P(U \cup V) = 0.26 + 0.37 \]
\[ P(U \cup V) = 0.63 \]
**c. Finding \( P(U | V) \)**
For mutually exclusive events, the conditional probability \( P(U | V) \) is given by:
\[ P(U | V) = \frac{P(U \cap V)}{P(V)} \]
Since \( P(U \cap V) = 0 \) (from part a),
\[ P(U | V) = \frac{0}{0.37} = 0 \]
So, the answers are:
- \( P(U \cap V) = 0 \)
- \( P(U \cup V) = 0.63 \)
- \( P(U | V) = 0 \)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 1 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