Mrs. Jones hears a knock at the door. She opens the door and finds 3 police officers asking if they can come into her home to talk about...

I assume that you are asking whether this arrest is legal. If so, the answer is yes, it is perfectly legal.  A police officer can arrest anyone at any time if he or she has probable cause to believe that they have committed a crime.

In this case, your question has to do with whether the officers needed a warrant to officially “see” the bomb and arrest Mrs. Jones for it. The answer is that...

I assume that you are asking whether this arrest is legal. If so, the answer is yes, it is perfectly legal.  A police officer can arrest anyone at any time if he or she has probable cause to believe that they have committed a crime.

In this case, your question has to do with whether the officers needed a warrant to officially “see” the bomb and arrest Mrs. Jones for it. The answer is that they did not need a warrant.  The officers were in the house legally.  Mrs. Jones had allowed them to come in of her own free will.  The officers saw the bomb legally.  It was out in plain view.  When officers are legally in a place, they are allowed to officially “see” anything that is plain sight.  If the officers had started looking around the house, poking into places that were not in plain sight, the search would be illegal.  If, for example, the bomb had been in a closet and the officers had opened the door to the closet without being given permission, they could not legally have arrested Mrs. Jones.  However, the bomb was out in plain sight, where the officer was able to see it without snooping around. Therefore, it was legal for the officer to see it and to arrest Mrs. Jones for having it.