> If you pick a number 1-10 100 times completely randomly and each number has a 10% chance of being picked each time (so picking a 7 once doesn’t decrease the likelihood of picking it on the next try) why won’t you end up with 10 of each number?
It may be easier to see how this works with smaller numbers. You flip a coin twice. It’s either heads or tails, 50% probability, and the two flips are independent. Your question is “why don’t you end up with exactly 1 heads and 1 tails?”
Flip the coin once. Suppose (for the sake of argument) that it lands on heads. You flip it again. There is nothing to influence the coin to land tails here – it’s still 50-50 whether it lands heads or tails.
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