Imagine throwing a coin N times, let x be the number of heads. Show that $\frac{x}{N} \rightarrow \frac{1}{2}$, as N increases.
So I know that a coin toss follows the binomial distribution with $p = q = \frac 12$ (we have a fair coin).
So then the probability of getting x heads after n tosses would be ${n}\choose{x}$$\left(\frac{1}{2}\right)^n$.. but I don't know how to use that to solve my question... The only other thing I could think of was that the expected value of the binomial distribution is equal to np. So then dividing this by n gives p... but this seems to trivial to be right.