MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.](https://content.bartleby.com/qna-images/question/97b5df25-1667-438a-b46e-c2a0d1ae7c86/19fc7998-ae4e-4758-8052-657e2710ce4e/jub8c8g_processed.jpeg)
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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