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## Homework Statement

You throw a coin a 100 times, what's the probability of getting 50 tails?

## Homework Equations

## The Attempt at a Solution

We have n=100 , p=1/2, q=1/2 and k=50 we substitute in the first equation we get:

P= 100!/ (50! * 50!) * (1/2)^100

The factorials are not simple to calculate so i used Stirling formula ( logarithmic approximation) and i found that Log P=0 so P=1 which i think is incorrect because 1 is the sum of all the probabilities...so where is my mistake?