  The method of defining quantum joint probabilities of two events is applied
to a multimode system of trapped Bose-condensed atoms. The coherent modes are
generated by modulating the trapping potential with an alternating field with a
frequency in resonance with a transition frequency between two coherent modes.
The system is subjected to nondestructive measurements randomly influencing the
phase difference of the modes. The joint probability of observing two events,
corresponding to the observation of two states, is calculated by employing the
channel-state duality. The interference term in the joint probability can arise
when the composite events form an entangled prospect and the system state is
also entangled. This interference is due to the uncertainty induced by
nondestructive measurements.
