What type of airplane may not carry passengers for compensation or hire?

The correct answer is that primary category aircraft may not carry passengers for compensation or hire. This is because primary category aircraft are specifically designed for flight training, personal use, or certain other non-commercial purposes. They are often used for training pilots and are restricted from engaging in commercial operations, including carrying passengers for compensation.

In contrast, limited category aircraft can be used for compensation under certain conditions, as they may be utilized for specific operations like production and exhibition flights. Utility category aircraft have more flexibility in terms of operations, allowing for a mix of commercial and private use. Experimental category aircraft are typically not used for commercial passenger transport either, but they are mainly intended for testing new designs or technologies and require special permits for operation.

Understanding these distinctions helps clarify why primary category aircraft are the answer, as they are clearly defined for specific uses that exclude commercial passenger transport.