Probability Question

Verance

Looking to find the probability of a horse to finish in a certain position in a horse race if the probability of winning is known.

Assuming probabilities of winning:
Horse 1 - 40%
Horse 2 - 20%
Horse 3 - 15%
Horse 4 - 10%
Horse 5 - 10%
Horse 6 - 5%

Would it be possible to calculate probability of Horse 1 coming third? Or Horse 4 coming 4th?

D-Generate

Yeah it would be possible to work it out but it would be well difficult and the complexity would scale pretty quickly as more horses are thrown in.

For the lazy approach I advise you to just get a quick and dirty answer by using a monte-carlo method to get the answer. If you alright at programming in MATLAB or R then should take you no more than 5 mins to do. Certainly quicker than working it out by hand.

MathsManiac

Of course, you'd have to make assumptions about how the other horses will finish given that one particular one comes first. For example, you may wish to assume that, among the horses who don't win, their probabilities of coming second are in direct proportion to their initial probabilities of winning the race.

In the absence of any other information, it's probably the best assumption you can make, but it's not really likely to be true in reality, I would guess.

R0UF

No, it is not possible to any level of accuracy based on the information provided.

It may be worth your time investigating the Harville formula.