In a large population, 65% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? Give your answer as a decimal (to at least 3 places) or fraction.
In a large population, 65% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? Give your answer as a decimal (to at least 3 places) or fraction.
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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![**Problem Statement:**
In a large population, 65% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that at least one of them has been vaccinated?
**Instructions:**
Give your answer as a decimal (to at least 3 places) or fraction.
**Solution Guide:**
To solve this problem, first calculate the probability that none of the selected people have been vaccinated. The probability that a single person has not been vaccinated is \(1 - 0.65 = 0.35\).
1. **Probability none are vaccinated:**
\[
P(\text{none}) = 0.35^5
\]
2. **Probability at least one is vaccinated:**
\[
P(\text{at least one}) = 1 - P(\text{none})
\]
Using these formulas, you can find the probability of at least one person being vaccinated when selecting 5 people from the population.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F97b5df25-1667-438a-b46e-c2a0d1ae7c86%2F19fc7998-ae4e-4758-8052-657e2710ce4e%2Fjub8c8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
In a large population, 65% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that at least one of them has been vaccinated?
**Instructions:**
Give your answer as a decimal (to at least 3 places) or fraction.
**Solution Guide:**
To solve this problem, first calculate the probability that none of the selected people have been vaccinated. The probability that a single person has not been vaccinated is \(1 - 0.65 = 0.35\).
1. **Probability none are vaccinated:**
\[
P(\text{none}) = 0.35^5
\]
2. **Probability at least one is vaccinated:**
\[
P(\text{at least one}) = 1 - P(\text{none})
\]
Using these formulas, you can find the probability of at least one person being vaccinated when selecting 5 people from the population.
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