Question 614883: Rick is at a horse race and decides to predict the exact order in which the horses will finish first, second, and third. If 11 horses are racing, and each horse is equally likely to win, what is the probability that Rick will guess correctly?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the probability that rick will guess correctly will be equal to:
1 / 11p3 = 1 / 990
There are 990 possible permutations of obtaining 3 horses out of 11 where order matters.
he can only pick one of them.
this makes the probability of getting it right 1 / 990.
it might be easier to see if we use only 4 horses and we try to pick first and second place out of them.
the number of possible permutations is equal to 4p2 = 12.
if the horse are labeled a, b, c, d, then those permutations are:
ab and ba
ac and ca
ad and da
bc and cb
bd and bd
cd and dc
that's 12 possible permutations.
he can pick only one of them.
let's say he picks a is first and d is second.
that's one out of the 12 possible permutations.
with 11 horses, the numbers get very much larger and it's harder to see the individual possibilities but the same concepts apply so you can be reasonably sure that the answer is correct.
1 out of 990 is a probability of .001010101.. which is less than 0.2%
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