Let $X$ be a random variable defined on a probability space $(\Omega , \mathcal{A} , \mathbf{P})$ with values in $\mathbf{N}$ and admitting an expectation $\mathbf{E}(X)$ and a variance $\mathbf{V}(X)$.\\
Show that if $\mathbf{E}(X) \neq 0$, then $\mathbf{P}(X = 0) \leq \frac{\mathbf{V}(X)}{(\mathbf{E}(X))^{2}}$.\\
Hint: note that $(X = 0) \subset (|X - \mathbf{E}(X)| \geq \mathbf{E}(X))$.