Final answer:
The contaminated gloves should be disposed of in a biohazard bag, and the sharps should be disposed of in a puncture-proof biohazard sharps container.
Step-by-step explanation:
The correct statement that describes the disposal of the waste in this situation is: Dispose of the contaminated gloves in a biohazard bag; then dispose of the sharps in puncture-proof biohazard sharps container.
When a phlebotomy needle comes out of the patient's arm and the gloves become grossly bloody, there is a risk of exposure to bloodborne pathogens.
Therefore, it is important to dispose of the contaminated gloves in a biohazard bag, which is specifically designed to safely contain and dispose of hazardous materials. The sharps, in this case, should be disposed of in a puncture-proof biohazard sharps container to prevent any accidental injuries from the needle.