Find the probability of the indicated event if P(E)=0.30 and P(F) = 0.40. Find P(E or F) if P(E and F) = 0.20. P(E or F) = (Simplify your answer.)
Find the probability of the indicated event if P(E)=0.30 and P(F) = 0.40. Find P(E or F) if P(E and F) = 0.20. P(E or F) = (Simplify your answer.)
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
![**Educational Content: Probability of Combined Events**
To calculate the probability of either event \( E \) or event \( F \) occurring, when the probabilities of individual and combined events are provided, use the following formula:
\[
P(E \text{ or } F) = P(E) + P(F) - P(E \text{ and } F)
\]
In this problem, the given probabilities are:
- \( P(E) = 0.30 \)
- \( P(F) = 0.40 \)
- \( P(E \text{ and } F) = 0.20 \)
**Task:**
Find \( P(E \text{ or } F) \).
**Solution Steps:**
1. Substitute the given probabilities into the formula:
\[
P(E \text{ or } F) = 0.30 + 0.40 - 0.20
\]
2. Calculate the result:
\[
P(E \text{ or } F) = 0.50
\]
**Conclusion:**
The probability of either event \( E \) or event \( F \) occurring is \( 0.50 \).
**Note:** Remember to simplify your answer when necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a871af6-0cb4-4831-8890-4d60934ca80c%2F9039ca8c-df85-4b1d-a3f0-588e4d4bc7bf%2Fh4tkawt_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Probability of Combined Events**
To calculate the probability of either event \( E \) or event \( F \) occurring, when the probabilities of individual and combined events are provided, use the following formula:
\[
P(E \text{ or } F) = P(E) + P(F) - P(E \text{ and } F)
\]
In this problem, the given probabilities are:
- \( P(E) = 0.30 \)
- \( P(F) = 0.40 \)
- \( P(E \text{ and } F) = 0.20 \)
**Task:**
Find \( P(E \text{ or } F) \).
**Solution Steps:**
1. Substitute the given probabilities into the formula:
\[
P(E \text{ or } F) = 0.30 + 0.40 - 0.20
\]
2. Calculate the result:
\[
P(E \text{ or } F) = 0.50
\]
**Conclusion:**
The probability of either event \( E \) or event \( F \) occurring is \( 0.50 \).
**Note:** Remember to simplify your answer when necessary.
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