You flip a fair coin 10,000 times. Approximate the probability thatthe difference between the number of heads and the number of tails is at most 100.

E[X] = (np) (p + (1-p)) ^ (n-1)

With n = 10,000 and p=0.50 we get

E[X] = (10,000*0.50) (0.50 + (1-0.50)) ^ (10,000-1)

E[X] = 5,000 (1)

So assuming the coin is fair (p=50%), then we can expect to get heads 5,000 times when the coin is tossed 10,000 times.