Under what conditions can a private pilot carry passengers for compensation or hire?

A private pilot is prohibited from carrying passengers for compensation or hire under any circumstances. This rule exists to ensure that private pilots operate within the limitations of their certification, which primarily focuses on personal flying and not commercial activities. The rationale is that engaging in compensated flight operations requires a higher level of training and licensing that falls under the purview of commercial pilot certification.

The other choices imply circumstances where a private pilot could potentially receive compensation, which is not aligned with the regulations governing private pilot privileges. Therefore, the correct understanding is that a private pilot cannot carry passengers for compensation or hire at all.