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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Nothing, its just the law of large numbers. Even if you have random unrelated events, try a bunch of times and the probabilities turn into fraction.
Or rather thats how probabilities are introduced. If you want to know the probability of an event try more and more and see what fraction of the results end in your event. What that fraction is approaching is the probability.
So flip a coin, once. H or T? Hard to say. Flip a coin 1 000 000 times. About 500 000 H and 500 000 T. Once you have enough attempts statistics allow for probabilistic thinga to be predictable. Since everything that can happen does happen and the question is how much something has happened.
If you throw a die 10 times its hard to predict how many sixes you got. But throw it 6 million times and saying its 1 million sixes is extremely accurate. With large numbers we are not asking if something has happened, we are asking how much the event happened.
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