Final answer:
Used needles and syringes are the most likely way to transmit an HIV infection. HIV is not transmitted through casual contact or by sitting on a public toilet seat.
Step-by-step explanation:
The most likely route of HIV transmission among the options listed is through used needles and syringes (option b). HIV can be spread through contaminated needles when they are shared by drug users. This is why it is important to never share needles or syringes.
HIV is not transmitted through casual contact with an infected patient (option c) or by sitting on a public toilet seat (option d). These are common misconceptions and HIV is not spread through day-to-day contact in workplaces, schools, or social settings.
Although it is theoretically possible for HIV to be transmitted through blood used for transfusion (option a), the risk is extremely low due to careful screening of blood donors and blood products in many countries. However, in poor nations where screening is less rigorous, the risk may be higher.