I'm trying to determine the probability that I'll "place" within certain percentage in a given contest against other competitors. The two specific examples I can provide that I do not know how to determine the answer to are as follows:
Example 1: I'm entering a "head to head" contest. I know that I place 1st (win) head to head contests 70% of the time. The individual I'm competing against places 1st (wins) head to head contests 60% of the time. How do I determine the probability that I'll beat this competitor in a head to head contest?
Example 2: I'm entering a contest where there are 10 competitors. To win in this contest, I need to place in either 1st, 2nd, 3rd or 4th place. I know that I typically place within the top 37% of all contests of this type (average figure for all contests of this type I've entered). I know that the other 9 competitors entering have the following overall placement %'s: top 10%; top 20%; top 30%; top 40%; top 50%; top 60%; top 70%; top 80%; top 90%. How do I determine the probability that I'll place in the top 40% (in either 1st through 4th place).
I know it is typically good etiquette to explain how far I've gotten in a solution, but I honestly do not even know where to begin. Appreciate any assistance this community can offer.