Applying result R5324: Conditional expectation of a random real number conditioned on itself, we have \begin{equation} \mathbb{E}(X \mid Z) = \mathbb{E}(X \mid X) \overset{a.s.}{=} X \end{equation} while from the results

(i)	R5325: Conditional expectation of random real number conditioned on an independent random real number
(ii)	R5283: Expectation of a standard bernoulli random boolean number

we know that \begin{equation} \mathbb{E}(Y \mid Z) = \mathbb{E}(Y \mid X) \overset{a.s.}{=} \mathbb{E} Y = \frac{1}{2} \end{equation} Clearly, $X \overset{d}{\neq} 1 / 2$. $\square$