# How do 1s and 2p orbitals overlap?

In the following figure

we can see that the p-orbitals overlap 1s orbital (though relatively very little). How can an electron in p-orbital, be simultaneously in the 1s orbital at any given point in space and time?

The question is interesting, but slightly ill-defined. If you take s and p orbitals as a solution of Schrodinger equation of hydrogen-like atom, then they are eigenfunctions of Hamiltonian, therefore are orthogonal. That means - no overlap. Do not be misled by the figure, if you do the math properly, $\langle1s|2p\rangle = 0$.
It is important to know that the overlap must be performed with the wave functions $\psi_j(\vec{r})$, not the density, $\rho_j(\vec{r}) = \psi_j(\vec{r})^* \psi_j(\vec{r})$. Wave functions have signs; they oscillate, as these oscillations encode the momentum distribution $\rho_j(\vec{p})$.
When you calculate the overlap between $\psi_s(\vec{r})$ and $\psi_p(\vec{r})$, $\int_V \psi_s(\vec{r}) \psi_p(\vec{r}) dV$ ($V$ is the volume) you should remember that the lobes of the "p" wave function have different signs, while the spherical $s$ wave function keeps the same sign over the surface of the sphere. Therefore, the integral has two identical but opposite (different sign) contributions that cancel the overlap.