Probability of 40-Difference Heads/Tails After 1000 Coin Tosses

[alpignolo]

If I throw 1000 times a coin what is the probability to have at least one time a difference between heads and tails of 40.
thank you for yours help

 

[EnumaElish]

If n is the number of heads, m is the number of tails, how would you express your question arithmetically?

 

[mathman]

The problem you stated is an example of a random walk with one barrier problem. You can find a discussion in any standard probability text. For example Feller (Vol I) is a very good, although old test.

 

[alpignolo]

I'm sorry but I don't see the solution, It would be easy if I have to stimate the probability after n flip but I have to calculate it dinamically trough the n flips.
I thougt to make tehe product from 40 to n-40 of (1-Bin(0.5)) but i don't know if is right.
With 1000 flip --> p=1-0.126 to see a difference of 40 during the test

Thank you