I am calculating the reduced density matrix of a bipartite system, I ended up getting that it was the sum of two density matrices of pure states each with a probability $1/3$. My understanding was that the coefficients in this ensemble should add up to $1$. But perhaps this is only for density matrices of whole systems and not for a reduced density matrix? So have I made an error in the calculation (I don't think I have) or the result I got possible?