Question

A particular nucleus in a large population of identical radioactive nuclei did survive 5 half life of that isotope then the probability that this surviving nucleus will survive the next half life

Answer 1

Probability for every single half time is 1/2
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what this exercise shows you, is that the radiactive nucleus as a 50% chance to decay during its half-life period, but if it has not decayed, it remains unchanged: it has same number of protons and neutrons, same instability, and so during the next period it still have a 50% probability to decay, and so on.