Here's the scenario:

It is known that 11% of people on average have property A.

If I test people with characteristic H and find that 100% of them have property A, how many would I have to test to be 95% confident that this is not just by chance? What about 99% confidence? How confident could I be with a sample size of just 2?

Please show workings, I would like to understand this. Thank you.