what id the probability that you will have 1 out of 55 topics in common with a stranger

Question

For simplicity, assume that the probability that your details match for any given topic is 1/40 and is independent from one topic to the next. If you discuss ten topics, how surprising would it be to find that you match on at least one of them?

Answer 1

The probability of not matching any topic is (39/40)¹⁰=0.7763 approx, so the probability of matching at least one is 1-0.7763=0.2237, or about 22.4%, not that surprising (almost 1 in 4).

If the probability is 1/55 then this becomes 1-(54/55)¹⁰=0.1676.