This is my first question so apologies if its unclear/vague.
There exists a contest with me in it, and $5$ others, thus $6$ people in total, along with $5$ prizes. A person can only win one prize, and once they do, they're out of the contest. Winners are chosen at random.
So, what is the chance of me winning at a prize?
My initial thought was: $\frac16$ chance initially, then $\frac15$ if I don't win the first time, $\frac14$ if I don't win the second, ect. as people are removed once they win, resulting in $\frac16+\frac15+\frac14+\frac13+\frac12 = 1.45$ which is $145$%.
This is greater than $100$%, and obviously I am not guaranteed to win as I can be the $1$ loser, so how do you find the correct probability?
Edit: All of you have been extremely helpful. Thank you!