Probability and current density of a particle (15 min)

Assume that a particle in an interval $[-L/2,L/2]$ is described by a wave function

$$\Psi(x,t)=\frac{1}{\sqrt{L}}e^{i(kx-\omega t)}.$$

What are the probability density $\rho(x,t)$ and the current density $j(x,t)$ for this wave function ? How can one express the current density by the probability density and the velocity? What is the probability to find the particle a) anywhere in the interval $[-L/2,L/2]$; b) in the interval $[-L/2,0]$; c) in the interval $[0,L/4]$ ?