# Is entanglement a classical phenomena?

If I have an entangled state shared between two parties Alice and Bob $$\frac{1}{\sqrt{2}}|00\rangle+\frac{1}{\sqrt{2}}|11\rangle....(1)$$ then the reduced density operator of Alice's side is $\frac{I}{2}$, that is Alice's qubit is in mixed state. But being in a mixed state is a classical phenomena. By classical phenomena I mean when we write density operator for mixed state that can be in either of $\{|\psi_i\rangle\}$ states with probability $p_i$, we know that system is exactly one of the states but just don't know which .Such uncertainties are due to defects in device etc is a classical phenomena. So is entanglement due to the reason Alice's/Bob's reduced density operator is mixed ( which is a classical phenomena if I am not wrong )?
Sorry if I could not put this more properly in words.

$$|\psi\rangle_A \otimes |\psi\rangle_A$$