Understanding Probability and Equality in Binary Choices

[jk22]

Suppose we have 2n binary choices. Then the probability of having the same number of results is :

C(2n,n)/2^(2n) ?

I don't know if this is true, since for the case n=1million, we have a probability as high as 1/2000, which seems quite important ?

 

[mathman]

Suppose we have 2n binary choices. Then the probability of having the same number of results is :

C(2n,n)/2^(2n) ?

I don't know if this is true, since for the case n=1million, we have a probability as high as 1/2000, which seems quite important ?

Your estimate seems about right. What is that a concern?

 

[jk22]

this was about votations : if we suppose 2 million 1 people vote a law then the highest probability is that only 1 voice makes the difference. I heard some people intepret this as there exist a sort of hidden dictator, but in fact we don't know who made the balance choice.