Which kind of analysis is it when the IC weighs the potential danger to firefighters against the likelihood of saving someone inside?

The correct choice is the risk-benefit analysis. This type of analysis involves the Incident Commander (IC) assessing the potential risks to firefighters as they engage in a rescue operation against the benefits of possibly saving a life inside a structure.

In fireground operations, the IC must consider various factors, including the urgency of the rescue, the conditions within the environment, and the safety of the firefighting personnel. By evaluating these elements, the IC can make informed decisions about whether to proceed with a rescue attempt, ensuring that the safety of firefighters is prioritized while also striving to protect lives.

Risk-benefit analysis is foundational in emergency service operations, as it encapsulates the balancing act between taking necessary actions to save lives versus ensuring that those actions do not unduly endanger the responders involved. This approach is critical for maintaining operational safety and effectiveness during crisis situations.