What is the probability of the first racer winning first place?

[moonman239]

For example, the ratio of times he's won first place to the times he hasn't is 8 to 2. His average time is 2 minutes 10 seconds. His leading competitor has a first-place-to-non ratio of 8 to 3, and has an average time of 2 minutes and 11 seconds. The total time (and ratio) of the last 3 competing cars is 17 to 5, with an overall average time of 6 minutes and 10 seconds. What is the probability that the first racer will win first place?

 

[moonman239]

I think I have an equation:

p = (x/(x+y) + (ato/at) / n
where
x = the number of times the racer got first place
y = the number of times the racer did not
at = the average time it took for the racer to complete previous races
ato = the average time it took for all competitors to complete previous races
n = the number of competitors.