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]
