TeX source:

\Pr\{m\} = \sum_i\Pr\{m|i\}p_i = \sum_ip_i\text{tr}(\mathbf{M}_m^\dagger\mathbf{M}_m|\psi_i\rangle\langle\psi_i|) = \text{tr}(\mathbf{M}_m^\dagger\mathbf{M}_m\rho).