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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Every single atom of uranium 238 has at any time a very small chance of decaying. That rate of decay just happens to coincide with half of it decaying every 4.5 billion years. The uranium that hasn’t decayed has essentially just been “lucky” so far, and probability dictates how that distribution is met.
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