We throw a die as many times as we thrown $k$ tails and $k$ heads (it can't be one after another). Let $X$ be a number of throwing. Set the distribution of $X$ and $\mathbb{E}X$
So, I've started from setting the set value of $X$ it is: $\left\{2k, 2k+1, 2k+2, \ldots , \infty \right\}$
Next $\mathbb{P}(X=2k)=\frac{ {2k \choose k} }{2^{2k}}$. And I've noticed it would be hard to set the rest of probablilities. Thats why I think to calculate $\mathbb{P}(X>x)=$ but I've stacked in it. Can you help me?