Number of potential winners in a contest of 34 rounds.

Question

I am one of 10 players in a game. We each have an equal chance to win the game (1 winner a round). There are 34 rounds. What percentage of players win at least one round?

Answer 1

This looks similar to the birthday problem that uses the pigeonhole principle. If you don't know about it it is interesting and may help you with your problem. I would think that the number in your problem is going to be real close to 100%!

In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.