eli5: if a certain phenomenon occurs in 5% of a sample, does that mathematically mean it’s 5% likely to happen for any member of said sample? if yes, how?

Question

eli5: if a certain phenomenon occurs in 5% of a sample, does that mathematically mean it’s 5% likely to happen for any member of said sample? if yes, how?

In: 1

Answer 1

No.

If I have 20 people and 1 of them is sick, it means 5% of people in the sample are sick. It does not mean that if I pick a person from the sample at random, there is a 5% chance they will.get sick, it means if I pick a random person there’s a 5% chance I get the sick one.