Again returning to the birthday problem analogy: in a room with merely 23 people, the chances that two people will share some birthday are 50/50. But the chances that you will match any one given person are 1 in 365 (actually not quite, because birthdays are not distributed in a completely even fashion, but ignore that for now).

The chances that you will match someone in a room aren’t 50/50. I’m not a statistics expert, but I believe they are 1 in (365 divided by the number of people in the room). So if there are 23 people in the room, the chances that two people will share a birthday a 50/50, but the chance that you will match someone are 1 in 365/23, or roughly 1 in 16.

I’m employing common sense and not higher math skills here, so if I’m wrong, feel free to tell me.