Find P(A or B or C) for the given probabilities
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
![Find \( P(A \text{ or } B \text{ or } C) \) for the given probabilities.
- \( P(A) = 0.36 \)
- \( P(B) = 0.25 \)
- \( P(C) = 0.16 \)
- \( P(A \text{ and } B) = 0.12 \)
- \( P(A \text{ and } C) = 0.03 \)
- \( P(B \text{ and } C) = 0.05 \)
- \( P(A \text{ and } B \text{ and } C) = 0.01 \)
\[ P(A \text{ or } B \text{ or } C) = \]
**Explanation:**
To find \( P(A \text{ or } B \text{ or } C) \), you can use the principle of inclusion-exclusion:
\[
P(A \text{ or } B \text{ or } C) = P(A) + P(B) + P(C) - P(A \text{ and } B) - P(A \text{ and } C) - P(B \text{ and } C) + P(A \text{ and } B \text{ and } C)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F508ee786-e013-45c0-a264-dadcc72c168c%2F04442b64-5e31-41a1-bcf5-2cb34d83a099%2Fikua0g7.jpeg&w=3840&q=75)
Transcribed Image Text:Find \( P(A \text{ or } B \text{ or } C) \) for the given probabilities.
- \( P(A) = 0.36 \)
- \( P(B) = 0.25 \)
- \( P(C) = 0.16 \)
- \( P(A \text{ and } B) = 0.12 \)
- \( P(A \text{ and } C) = 0.03 \)
- \( P(B \text{ and } C) = 0.05 \)
- \( P(A \text{ and } B \text{ and } C) = 0.01 \)
\[ P(A \text{ or } B \text{ or } C) = \]
**Explanation:**
To find \( P(A \text{ or } B \text{ or } C) \), you can use the principle of inclusion-exclusion:
\[
P(A \text{ or } B \text{ or } C) = P(A) + P(B) + P(C) - P(A \text{ and } B) - P(A \text{ and } C) - P(B \text{ and } C) + P(A \text{ and } B \text{ and } C)
\]
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