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In the 131st running of the Kentucky
Derby in 2005, there were 20 contenders.
If all 20 horses have an equal chance of
winning and 3 of the horses are female,
what is the probability that a female
horse places first, second, and third? WORK PLEASE!
 one year ago
 one year ago
In the 131st running of the Kentucky Derby in 2005, there were 20 contenders. If all 20 horses have an equal chance of winning and 3 of the horses are female, what is the probability that a female horse places first, second, and third? WORK PLEASE!
 one year ago
 one year ago

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zeppBest ResponseYou've already chosen the best response.1
Uh.. I think that 1st: 3/20 (3 chances on 20) 2nd: 3/19 (3 chances on 19, since a male horse already won) 3rd: 3/18 (3 chances on 18, since 2 male horse already won) I'm really not sure about my work, I haven't done any probability question for almost 2 years , so I'm a little bit rusty :s @KingGeorge
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
For a female horse to place first, the chance is indeed 3/20. For a female horse to place second, you have to add the probability that a female horse placed first and second, and the probability that a female horse only placed 2nd. That would be \[{3\over20} \cdot {2\over19} + {17\over20}\cdot{3\over19}\] For a female horse placing third we need to consider all 4 possibilities of FFF, FMF, MFF, MMF. This results in a probability of \[\left({3 \over 20}\cdot{2 \over 19}\cdot{1 \over 18}\right)+\left({3 \over 20}\cdot{17 \over 19}\cdot{2 \over 18}\right)+\left({17 \over 20}\cdot{3 \over 19}\cdot{2 \over 18}\right)+\left({17 \over 20}\cdot{16 \over 19}\cdot{3 \over 18}\right)\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
If you just want the probability of all three places being claimed by a female horse, then it's just \[{3 \over 20}\cdot{2 \over 19}\cdot{1 \over 18}\]
 one year ago

zeppBest ResponseYou've already chosen the best response.1
Oh I see, thanks for the explanation :D
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
You're very welcome.
 one year ago
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