Let $X \in \text{Gaussian}(0, 1)$ be a D211: Standard gaussian random real number.
Let $t \in (0, \infty)$ be a D993: Real number.

Then

(1)	\begin{equation} \mathbb{P}(X > t) \leq \frac{1}{\sqrt{2 \pi}} \frac{1}{t} e^{- \frac{1}{2} t^2} \end{equation}
(2)	\begin{equation} \mathbb{P}(X < -t) \leq \frac{1}{\sqrt{2 \pi}} \frac{1}{t} e^{- \frac{1}{2} t^2} \end{equation}
(3)	\begin{equation} \mathbb{P}(|X| > t) \leq \sqrt{\frac{2}{\pi}} \frac{1}{t} e^{- \frac{1}{2} t^2} \end{equation}

Let $X \in \text{Gaussian}(0, 1)$ be a D211: Standard gaussian random real number.
Let $t \in (0, \infty)$ be a D993: Real number.

Then

(1)	\begin{equation} \mathbb{P}(X > t) \leq \frac{1}{\sqrt{2 \pi}} \frac{1}{t} \exp \left( - \frac{1}{2} t^2 \right) \end{equation}
(2)	\begin{equation} \mathbb{P}(X < -t) \leq \frac{1}{\sqrt{2 \pi}} \frac{1}{t} \exp \left( - \frac{1}{2} t^2 \right) \end{equation}
(3)	\begin{equation} \mathbb{P}(|X| > t) \leq \sqrt{\frac{2}{\pi}} \frac{1}{t} \exp \left( - \frac{1}{2} t^2 \right) \end{equation}