Three percent of the students at Lincoln High are in orchestra, 5% are in band, and 1% are in both. If a student is selected at random, what is the probability that the student is in orchestra or band? %
Three percent of the students at Lincoln High are in orchestra, 5% are in band, and 1% are in both. If a student is selected at random, what is the probability that the student is in orchestra or band? %
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Finding the Probability of Students in Orchestra or Band**
**Problem Statement:**
Three percent of the students at Lincoln High are in the orchestra, 5% are in the band, and 1% are in both. If a student is selected at random, what is the probability that the student is in the orchestra or band?
**Solution:**
To solve this problem, we need to use the principle of inclusion-exclusion for the probability of the union of two events.
Let:
- \( P(O) \) = Probability that a student is in the orchestra = 3%
- \( P(B) \) = Probability that a student is in the band = 5%
- \( P(O \cap B) \) = Probability that a student is in both the orchestra and band = 1%
Using the principle of inclusion-exclusion, the probability that a student is in either the orchestra or the band is given by:
\[ P(O \cup B) = P(O) + P(B) - P(O \cap B) \]
Substituting the values, we get:
\[ P(O \cup B) = 0.03 + 0.05 - 0.01 = 0.07 = 7\% \]
Therefore, the probability that a student is in the orchestra or the band is:
**7%**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b8f79a9-b6a4-48ca-ab39-5a4f4172185c%2F07d1c0f8-982b-4849-89ac-3c26bcce9c0b%2Fnju3ubv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Probability of Students in Orchestra or Band**
**Problem Statement:**
Three percent of the students at Lincoln High are in the orchestra, 5% are in the band, and 1% are in both. If a student is selected at random, what is the probability that the student is in the orchestra or band?
**Solution:**
To solve this problem, we need to use the principle of inclusion-exclusion for the probability of the union of two events.
Let:
- \( P(O) \) = Probability that a student is in the orchestra = 3%
- \( P(B) \) = Probability that a student is in the band = 5%
- \( P(O \cap B) \) = Probability that a student is in both the orchestra and band = 1%
Using the principle of inclusion-exclusion, the probability that a student is in either the orchestra or the band is given by:
\[ P(O \cup B) = P(O) + P(B) - P(O \cap B) \]
Substituting the values, we get:
\[ P(O \cup B) = 0.03 + 0.05 - 0.01 = 0.07 = 7\% \]
Therefore, the probability that a student is in the orchestra or the band is:
**7%**
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