Some do, some don't.
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In the US, they can. For example, security at nuclear power plants is privatised in the US, and private companies hire armed security officers to man these posts.
No
Security guards jobs are extremely important these days. There are increasing incidences of people robbing and harming other people. We all want to feel safe and security guards give us that feeling of safety.
The US Border Patrol, part of Homeland Security.
Anywhere in the US
No. About half the households in US have guns. Not every gun owner in the US carries a gun. The exact stats are uncertain, but simple logic would demonstrate that it would be less than 50% of Americans that carry guns.
Yes. They would not be very effective against criminals with guns with just a badge.
NoAnother View: In some jurisdictions persons engaging in such work must be licensed (e.g.: security guards - special officers - private investigators - etc) and if you carry any weapons asociated with that line of work you you most certainly must be licensed to carry these weapons.
Yes. It may require a license or permit, but yes.
There is a lot of disapproval towards gun ownership in the US.
Other than security contractors (Blackwater/XE, Triple Canopy, Aegis Defence Services, et. al), no. Most of the civilian contractor positions there specifically prohibit carrying arms.