{"knowledge_schema": {"broad_category": "Physics \u2192 Nuclear Physics \u2192 Radioactive Decay", "refinement": "This problem involves understanding the exponential decay of radioactive atoms and calculating probabilities based on decay rates.", "specific_scope": "The focus is on determining the probability of decay of a single atom over a specified time interval, given its decay probability and the time elapsed without decay.", "goal": "Calculate the probability that the atom will decay in the next 150 minutes after having survived for 50 minutes."}, "summary": "This problem deals with the concept of radioactive decay, specifically the probability of an atom decaying over a given time period. Given that the atom has not decayed in the first 50 minutes, we need to calculate the probability of it decaying in the subsequent 150 minutes. This involves applying the principles of exponential decay and understanding that the probability of decay is independent of the time already elapsed."}