I've learned that representing a combination of two states, I simply need to take the tensor product of the states. For example:
The combination state is given by: $$ \left|\Psi\right>\otimes\left|\Phi\right>=\alpha_0\alpha_1\left|00\right>+\alpha_0\beta_1\left|01\right>+\beta_0\alpha_1\left|10\right>+\beta_0\beta_1\left|11\right> $$
"Mixing" them in a classical sense can be done by simply finding their density matrices, and adding them together weighed by their probabilities respectively:
Which gives us a mixed state.
Can I understand it as the combination state is EITHER $\left|\Psi\right>$ OR $\left|\Phi\right>$ and the mixed state is BOTH $\left|\Psi\right>$ AND $\left|\Phi\right>$?
If so, is it possible to calculate the probability of finding $\left|\Psi\right>$ in $(\left|\Psi\right>\otimes\left|\Phi\right>)$? (By my intuition, if the combination state is OR, then the probability should be just $1$?)