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All Hospitals and Medical care institutions follow something called "Universal Precautions" recommended by WHO. This means all body fluids are considered infective for HIV and other infectious disease (including) by default and hence the staff should take adequate precautions while handling them.
There is NO reason for any concern at all. The lab personnels who handle hundreds of samples will be definitely using gloves.
Urine sample containers are very often contaminated (especially in females). Everyone knows that, so they will be handling it with care.
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