This seems counter-intuitive, but it really is so. Remember that the fact that the host opens a box does not move the car - the original distribution is still in effect.
If you still have a problem with this, check a simulation program which I wrote in C. You shouldn't really need to run it, you can just read the source to assure yourself that it solves the correct problem.
Approvable answers were received from the following persons: (Sorry, list was lost in an Emacs screwup.)