Throw a fair die 100 times, what is the probability that you will get more than 75 tails?

Umm...A die has six faces, so what's "heads"?

You add up the binomial distribution for k = 76 to 100, i.e. (100 k) * p ^k * (1-p) ^ 100-k for p=1/2, where (100 k) is "100 choose k", the binomial coefficient. The idea is to figure out how many paths lead to each of the 101 final outcomes of the "tree" (which is defined by the "100 choose k" coefficients") and multiply each one by it's probability. Pascal's triangle makes things easy to think about.

Approximate a Binomial distribution by a normal distribution.

it should be (1/(2*76))