Let $T_1 \in \text{Exp}(\theta_1), \dots, T_N \in \text{Exp}(\theta_N)$ each be an D214: Exponential random positive real number such that

(i)	$T_1, \dots, T_N$ is an D2713: Independent random collection.

Let $k \in \{ 1, \dots, N \}$ be a D5094: Positive integer.

Then \begin{equation} \mathbb{P}(T_k = \min(T_1, \dots, T_N)) = \frac{\theta_k}{\sum_{n = 1}^N \theta_n} \end{equation}

Let $T_1 \in \text{Exp}(\theta_1), \dots, T_N \in \text{Exp}(\theta_N)$ each be an D214: Exponential random positive real number such that

(i)	$T_1, \dots, T_N$ is an D2713: Independent random collection

Let $k \in \{ 1, \dots, N \}$ be a D5094: Positive integer.

Then \begin{equation} \mathbb{P}(T_k = \min(T_1, \dots, T_N)) = \frac{\theta_k}{\theta_1 + \cdots + \theta_N} \end{equation}