2024 MI H1 Q7

In a large population, the proportion of people who wear glasses is \(62.1\)%. A group of \(9\) people is randomly chosen from the population.

1. Find the probability that exactly \(3\) of these people wear glasses.[1]
2. Find the probability that at least five of these people wear glasses.[2]

The health promotion board decides to study \(10\) of such groups chosen randomly from the population.

3. Find the probability that less than half of the groups have at least five people wearing glasses.[3]