Regarding probability bound of flip coins Suppose you flip a fair coin 10,000 time how can you characterize the distribution of the occurrence of head?
From the textbook, it says that $P[head>\frac{n}2 + k\sqrt{n}]$ < $e^{-{k^2/2}}$, why is that and what is the derivation? What theorem is this, we had only learn Bernoulli distribution and Chebyshev so far, it seem odd that the textbook would jump to such a conclusion without rigorous proof.
Thanks in advance 

This is one step beyond Chebyshev, a much tighter bound. Consider the Chernoff bound. http://en.wikipedia.org/wiki/Chernoff_bound
The sketch of the proof is as follows.
Start with Markov's bound
$\mathbf{P}(X \geq a) \leq \frac{\textrm{E}(X)}{a}$ . Take the exponential on both sides of the inequality,  $\mathbf{P}(X \ge a) = \mathbf{P}\left (e^{tX} \ge e^{ta}\right ) \le \frac{ E[e^{tX}]}{e^{ta}}$ . The rest follows.
