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I would like to calculate the probability that a yes/no vote among 3000 voters ends up in a tie - assuming voters cast their vote randomly.

Applying the principle of favorable_cases/total_cases I calculate that the total_cases are all the possible ways the people could vote, therefore all permutations of 2 elements by 3000 draws = 2^30

Now, how can I calculate the favorable_cases: so those permutations of the voting that result in the same number of yes and no votes.

Are there other, perhaps more suitable ways to approach this question?

In addition, how could we calculate the probability of any result for say 1499 yes votes to 1501 no?

Thanks for helping!

nest
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    You want the number of ways of getting $1500$ yes votes and $1500$ no votes in any order. It may be easier to do this as a binomial probability to get the same answer: what is the probability of $1500$ yes votes out of $3000$ total votes? – Henry Aug 03 '23 at 13:36
  • If this is a homework, you should tag it as [self-study]. – Tim Aug 03 '23 at 13:36
  • I answered this in my post in the duplicate thread and then applied that to an asymptotic analysis. – whuber Aug 03 '23 at 14:15
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    While the other question should already gives several answers, I would like to stress a point about the formulation of this question. "assuming voters cast their vote randomly". As is clear in the duplicate question, it matters according to what distribution one considers the randomness. It is not sufficient to just state that the vote is random, but it is also important to state how it is random. – Sextus Empiricus Aug 03 '23 at 14:31
  • @Henry yes that seems right. Could you elaborate on how to make this calculation? My math is not so good. Thanks! – nest Aug 03 '23 at 14:45

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