Suppose that 26% of people have a dog, 21% of people have a cat, and 13% of people own both. What is the probability that someone owns a dog or a cat? The probability of a person having a dog or a cat is 47 (Type an integer or a decimal.) CILE
Suppose that 26% of people have a dog, 21% of people have a cat, and 13% of people own both. What is the probability that someone owns a dog or a cat? The probability of a person having a dog or a cat is 47 (Type an integer or a decimal.) CILE
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
![**Problem Explanation:**
Suppose that 26% of people have a dog, 21% of people have a cat, and 13% of people own both. What is the probability that someone owns a dog or a cat?
**Solution:**
To find the probability that someone owns a dog or a cat, we can use the principle of inclusion-exclusion. The formula to find the probability of either event A or event B occurring (when they can overlap) is:
\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]
Here,
- \( P(A) \) is the probability of owning a dog.
- \( P(B) \) is the probability of owning a cat.
- \( P(A \text{ and } B) \) is the probability of owning both a dog and a cat.
Given:
- \( P(A) = 26\% = 0.26 \)
- \( P(B) = 21\% = 0.21 \)
- \( P(A \text{ and } B) = 13\% = 0.13 \)
Now, substituting these values into the formula:
\[ P(A \text{ or } B) = 0.26 + 0.21 - 0.13 \]
\[ P(A \text{ or } B) = 0.34 \]
So the probability that a person has either a dog or a cat is \(34\%\) or \(0.34\).
**Transcription of Graphs or Diagrams:**
There are no graphs or diagrams present in the given image.
**Conclusion:**
The probability of a person having a dog or a cat is 47.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F786a2b18-36fc-4a59-90dc-399df5403cec%2F9a929578-a5c0-46da-83df-b532df3aa16e%2Fni96qyd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Explanation:**
Suppose that 26% of people have a dog, 21% of people have a cat, and 13% of people own both. What is the probability that someone owns a dog or a cat?
**Solution:**
To find the probability that someone owns a dog or a cat, we can use the principle of inclusion-exclusion. The formula to find the probability of either event A or event B occurring (when they can overlap) is:
\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]
Here,
- \( P(A) \) is the probability of owning a dog.
- \( P(B) \) is the probability of owning a cat.
- \( P(A \text{ and } B) \) is the probability of owning both a dog and a cat.
Given:
- \( P(A) = 26\% = 0.26 \)
- \( P(B) = 21\% = 0.21 \)
- \( P(A \text{ and } B) = 13\% = 0.13 \)
Now, substituting these values into the formula:
\[ P(A \text{ or } B) = 0.26 + 0.21 - 0.13 \]
\[ P(A \text{ or } B) = 0.34 \]
So the probability that a person has either a dog or a cat is \(34\%\) or \(0.34\).
**Transcription of Graphs or Diagrams:**
There are no graphs or diagrams present in the given image.
**Conclusion:**
The probability of a person having a dog or a cat is 47.
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