What does uvok think about in the mornings? #Mathematics.

is the probability of 99 coin flips all coming up heads the same as at least 99 of 100 coin flips coming up heads?

no, and you can prove that by reducing the question to

is the probability of 1 coin flip all coming up heads the same as at least 1 of 2 coin flips coming up heads?

"and of course the probability of 1 coin flip head is .5 while the latter is... 1?... .5 + .5? Wait, this can't be right. Let me get pen and paper to draw a decision tree..."

(it's .75, 1 - .25 for P(both tails))