# Horse race:tilting the possibility

#### FilupSmith

So, today we were studying the introduction of probability. For me it is fairly simple (for now).

My question is something we discussed during class today.

When betting on a horse before a horse race - say, a race of 5 horses, the odds ARE NOT 1/5 because the odds are not equal (eg. one horse may be faster).

So, what about if you placed a bet AFTER the race, assuming you don't know anything about any of the horses nor the outcome?

The way I think about this is that before the race, the horses had different chances of winning - tilting the possibility of winning or losing, and that after the race, although they HAD altering chances, the new 'guessing' chance is now indeed 1/5, is it not?

I'm not sure what to think, so I hope you guys can help :)

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#### AbhiNature

In my opinion it would be wrong to consider finding probability of something once you know its outcome.

What is the probability of 2 of heart coming from a well shuffled 52 cards? That would be 1/52. Once a card is chosen there is no question of probability.

Though what can be said even after the card is chosen (irrespective of 2 of heart comes or not) is that the probability of 2 of heart coming was 1/52.

#### FactChecker

Gold Member
2018 Award
So, today we were studying the introduction of probability. For me it is fairly simple (for now).

My question is something we discussed during class today.

When betting on a horse before a horse race - say, a race of 5 horses, the odds ARE NOT 1/5 because the odds are not equal (eg. one horse may be faster).
If you know something that changes the 1/5 probability for each, that should be applied. If you don't know anything, then 1/5 is a good guess
So, what about if you placed a bet AFTER the race, assuming you don't know anything about any of the horses nor the outcome?

The way I think about this is that before the race, the horses had different chances of winning - tilting the possibility of winning or losing, and that after the race, although they HAD altering chances, the new 'guessing' chance is now indeed 1/5, is it not?
If you have no new information, there is no reason to change your original guess. That is true regardless of what you knew before the race.
Probability theory is best looked at as "guessing information" theory. You make a guess based on your current information, regardless of when the experiment took place. A tossed fair coin has a 0.5 probability of heads until you know more about it -- even if it was tossed earlier. There is a subject called Bayes' Theory that tells you how to adjust probabilities for your guess as you get more information or hints.

#### pbuk

You are talking about two different things.

When betting on a horse before a horse race - say, a race of 5 horses, the odds ARE NOT 1/5 because the odds are not equal (eg. one horse may be faster).
Here you are talking about the probability of each horse winning the race, and assuming there are differences between the horses' capabilities, the probability for each horse is different.

So, what about if you placed a bet AFTER the race, assuming you don't know anything about any of the horses nor the outcome?
Here you are talking about the probability of you picking the winning horse, and assuming you don't know about the differences between the horses' capabilities before the race the probability s 1/5. This does not change after the race: assuming you don't know which horse actually won the race the probability of choosing which one did win is 1/5.

#### FilupSmith

Ok. I wasn't sure. Thanks :)

~| FilupSmith |~

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