We are asked to calculate the probability that at least one out of five randomly selected people has been vaccinated, given that 52% of the population is vaccinated.

This is a classic problem that involves using the complement rule. To find the probability that at least one person has been vaccinated, we first calculate the probability that none of the five people selected have been vaccinated. We then subtract this probability from 1 to find the complement.

Steps:

1. Probability that one person has NOT been vaccinated: $P(\text{not vaccinated}) = 1 - 0.52 = 0.48$

2. Probability that none of the 5 people have been vaccinated (i.e., all 5 are not vaccinated): $P(\text{none vaccinated}) = 0.48^5$ $P(\text{none vaccinated}) = (0.48)^5 = 0.0486$

3. Probability that at least one person has been vaccinated: $P(\text{at least one vaccinated}) = 1 - P(\text{none vaccinated})$ $P(\text{at least one vaccinated}) = 1 - 0.0486 = 0.9514$

Thus, the probability that at least one of the five people has been vaccinated is 0.9514.

Would you like more details or further clarifications on this?

Here are 5 relative questions you could explore:

1. How does the probability change if 10 people are selected instead of 5?
2. What would be the probability if the vaccination rate was 70% instead of 52%?
3. How can we calculate the expected number of vaccinated people in a group of 5?
4. How would this problem be solved if we were looking for exactly 3 vaccinated individuals?
5. What is the significance of the complement rule in probability theory?

Tip: For "at least one" probability problems, using the complement rule (finding the probability of the opposite event and subtracting from 1) is often the easiest approach.