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In a large population, 54 % of the people have been vaccinated. If 4 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated?



Answer :

chibabykalu16

Answer:

0.955

Explanation:

The probability of at least one person being vaccinated in a group of 4, when 54% of the population is vaccinated, can be calculated by first finding the probability that none of the 4 are vaccinated and subtracting this value from 1.

[tex] \sf P(\text{At least one}) = 1 - P(\text{None})[/tex]

1. The probability of a person not being vaccinated is;

[tex] \sf1 - 0.54 = 0.46[/tex]

2. The probability that none of the 4 selected people are vaccinated is;

[tex] \sf 0.46^4[/tex]

3. Therefore, the probability that at least one person is vaccinated is;

[tex] \sf 1 - 0.46^4 = 0.955[/tex]

Tips:

  • When dealing with "at least one" probability questions, it's often easier to calculate the probability of the opposite event (none) and subtract it from 1.

  • Remember the complement rule: [tex]P(\text{At least one}) = 1 - P(\text{None})[/tex]

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