Assume the universe has $18 \times 10^{18}$ planets. (18,000,000,000,000,000,000) Assume there are 5 million nomadic alien races in star ships traveling around the universe landing on planets at random. What are the odds that 2 of those alien races will land on the same planet? (Assume each race only travels to a single planet then remains there until all races have moved) It's kind of the birthday problem. I have $18 \times 10^{18}$ possible birthdays. What are the odds that of 5 million people, any of us share the same date?
Also, assume that everyday those spacefarers (including race X) each travel to a new planet. How many days will it take before race X has a 1% chance of landing on a planet previously visited by another spacefaring race.
The number is close enough to $0$ that you can make some approximations: given any pair, the probability they coincide is $1/(18 \times 10^{18})$ and there are about $12.5 \times 10^{12}$ possible pairs so the expected number of coincidences is about $6.944 \times 10^{-7}$ and since this is small it is also the approximate probability of any coincidence.
Multiply the reciprocal of this by the logarithm of $\frac{1}{1-0.01}$ and you get about $14472$ for the number of attempts needed to get the probability of a single coincidence up to $1\%$.