When are you not allowed to drive a motorized bicycle on public roads?

You answered correctly. You are not allowed to drive a motorized bicycle on public roads if you do not have motor vehicle liability insurance or if the vehicle is not roadworthy. Liability insurance is legally required to cover any damages or injuries caused to third parties. A roadworthy condition is necessary to ensure the vehicle poses no danger to yourself or others. However, whether motor vehicle tax has been paid is not a requirement for being allowed to drive a motorized bicycle, which is why answer 3 is not correct. Always make sure your vehicle is insured and maintained before using it on public roads.