Randomness in physics is prominently observed in quantum mechanics, particularly with the behavior of electrons. Radioactive decay is another example of true randomness, where a uranium nucleus can remain stable for billions of years before unpredictably emitting an alpha particle. This decay process lacks a known cause, highlighting the inherent unpredictability in certain physical phenomena. Discussions also touch on the broader implications of randomness in the universe and its unpredictability. Overall, the conversation emphasizes the significance of randomness in understanding fundamental physical processes.