Probability and Odds

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ipeters

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Oct 23, 2019
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I'm having trouble with a question, and need some help:
A race track betting board has the following odds:
Horse A 9:2
B 6:1
C 11:3
D 19:2
E 10:1
F 13:2
A bet called a "triactor" is when you name the exact order of the first 3 horses in the race. What is the probability of winning the triactor?
 
ipeters said:
I'm having trouble with a question, and need some help:
A race track betting board has the following odds:
Horse A 9:2
B 6:1
C 11:3
D 19:2
E 10:1
F 13:2
A bet called a "triactor" is when you name the exact order of the first 3 horses in the race. What is the probability of winning the triactor?
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I'm having trouble with a question, and need some help
Excellent, someone finally understands our rules-Mazel Tov!
How can we help you? Can you please tell us where you are stuck? That way we know how you want to attack this problem and we can guide you to the answer. Please post your work as well. Thanks so much.
 
The odds are made according to how much money is bet on each horse. I do not think that these odds reflect the real odds of a given horse to win.

Are you asking for the probability of winning the trifecta if you randomly pick 3 horses?
 
I'm sorry, here's what I was trying to do:
It is taken from a textbook and I left (when I retyped) out that the odds are odds against. I interpreted it as if I pick the 3 most likely, what is the probability they will win. I was picking the probabilities for the top 3 horses based on odds. But I thought that those probabilities were for 1st place finishing. The 3 most likely are horse are A, B, C, with C being the most likely. So, I found P(C) = 3/14 and then wanted to multiply by P(A) and P(B). For P(A) I though I should use 1-P(C) because I was looking for the probability of A winning with C out of the picture. And then, I'd do the same for B. However, I'm not sure this makes sense.
 
Here is my problem with your question. Suppose everyone knows that a particular horse would not come in 1st place. So no none in their right mind would bet on a horse which they know would not win. But does that mean that this horse will not finish in 3rd or 2nd place? Not at all, it might have an excellent chance to come in 2nd or 3rd place. So the horse with the worst odds (or is it the best odds??) has an excellent chance of being a horse in the trifecta.

I agree with you when you say that the odds/probabilities given are for 1st place.

Do you understand how the odds are made at the race track? I was a bit surprised when I found out but it does make sense.
Suppose for the 1st race there was $1000 in total bets. No matter which horse wins ALL the $1000 (minus a small percentage to the race track) goes to the people who bet on that horse. For example. If $100 was bet in total on horse 1, then the odds would be 10:1, that is for every $1 you bet, you will get back $10 (minus the fee to the track). Note that 10:1 is the same as 1000:100
If $500 in total was bet on horse number 2, then the odds will be 1000:500 or 2:1
 
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