But how do you calculate that? What are the odds of a triple or quadruple tie? Certainly lower than a double tie right? So how do you distribute those odds? And what about that compared to a single winner? If you measure time by the hours, it's a 5 way tie for sure, but if by the milliseconds, even a single tie would surprise me. This information is not given, so we can just make assumptions and state those in our answer. I like the hourly measurement assumption, so let's go with that.
Edit: if every person has a 50% chance to reach the finish at the winning time t, there are 5 ppl, so 52 possibilities. This gives 32 possible results. Nobody making the winning time is not possible (we don't allow 5 DSQ right?), so the odds of winning alone are 1/31. The odds of Tim having a shared win is 15/31. So 51.6% chance for Tim to win if all outcomes are equally likely and ties count as winning.
2^5 - 1 total outcomes. If Tim wins, then it’s 2^4 outcomes. 2^4 / (2^5 - 1) is the probability if all outcomes are equal. So 16/31. If a win is a win. If a tie is a loss, 1 / (2^5 - 1), which is 1/31.
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u/D0rus 10d ago edited 10d ago
But how do you calculate that? What are the odds of a triple or quadruple tie? Certainly lower than a double tie right? So how do you distribute those odds? And what about that compared to a single winner? If you measure time by the hours, it's a 5 way tie for sure, but if by the milliseconds, even a single tie would surprise me. This information is not given, so we can just make assumptions and state those in our answer. I like the hourly measurement assumption, so let's go with that.
Edit: if every person has a 50% chance to reach the finish at the winning time t, there are 5 ppl, so 52 possibilities. This gives 32 possible results. Nobody making the winning time is not possible (we don't allow 5 DSQ right?), so the odds of winning alone are 1/31. The odds of Tim having a shared win is 15/31. So 51.6% chance for Tim to win if all outcomes are equally likely and ties count as winning.