Probability of Median from a continuous distribution For a sample of size $n=3$ from a continuous probability distribution, what is $P(X_{(1)}<k<X_{(2)})$ where $k$ is the median of the distribution? What is $P(X_{(1)}<k<X_{(3)})$? 
$X_{(i)},i=1,2,3$ are the ordered values of the sample.
I'm having trouble trying to solve this question since the median is for the distribution and not the sample. The only explicit formulas for the median I know of are the median $k$ of any random variable $X$ satisfies $P(X≤k)≥1/2$ and $P(X≥k)≥1/2$, but I don't see how to apply that here.

This is also the probability of exactly one success in three trials, with probability $1/2$ of success on each trial.  Hence $\binom{3}{1} \left(\frac12\right)^3 = \frac38$.
