Since naturally occurring uranium (U-238) has a half life of 4.5 billion years, then it means half of the uranium on earth has decayed into lead by now. But why only half, and why that specific half? What was special about the particles that did decay? Were they different in some way?
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Each individual atom as a certain probability of decaying. Take a very large group of atoms and it becomes very predicable.
We made up the idea of a half life because its a simple way of classifying activity. Easier to say half will be gone in x years instead of each atom has a .00000…1% chance of decaying today.
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