you take 5 draws from U(9,15). Consider the random variable that equals the 2nd smallest of the 5 draws. What is the probability that this random variable is greater than 10?

Let$X_{1,} X_2, X_3, X_4, X_5$ be the sample drawn from the distribution$U\left(9,15\right)$. Denote the order statistics for it as follows:

$$\begin{gathered} X_{\left(1\right)}=\text{min}\left(X_{1,} X_2, X_3, X_4, X_5\right) \\ {X}_{\left(2\right)}={\text{the 2}}^{nd} smallest \\ {X}_{\left(3\right)}={\text{the 3}}^{rd} in order \\ {X}_{\left(4\right)}={\text{the 4}}^{th} in order \\ {X}_{\left(5\right)}=\text{max}\left(X_{1,} X_2, X_3, X_4, X_5\right) \end{gathered}$$

To find the probability of$X_{\left(2\right)}\ge 10$, first, it is required to define the pdf of$X_{\left(2\right)}$. Recall that the pdf is the probability of a random variable taking a particular value.