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

The correct answer to the question pertains to the concept of risk-benefit analysis. This type of analysis involves evaluating the potential dangers that firefighters might face in a given situation against the possible benefits of their actions, particularly concerning the likelihood of saving someone trapped or in danger.

In firefighting and emergency response, the Incident Commander (IC) must frequently assess the hazards present, including structural integrity, fire conditions, and the risks to personnel. This assessment helps determine whether the potential benefit—such as rescuing an individual—outweighs the risks involved in executing a rescue operation.

Ultimately, a thorough risk-benefit analysis allows the IC to make informed decisions that prioritize the safety of firefighters while also considering the objective of saving lives. This makes it a critical component of fire incident management and operational planning. In contrast, the other options may involve other frameworks of analysis but do not specifically address the balancing of risk to personnel and the potential for saving lives in the context presented by the question.