I have a truly burning question.
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?
In: 1
It may be easier to see what’s happening by taking a simpler case. Take a fair coin with a 50% chance of landing (H)eads and 50% chance of landing (T)ails and flip the coin 4 times.
After 4 flips, there are 16 possible outcomes:
HHHH / HHHT / HHTH / HHTT / HTHH / HTHT / HTTH / HTTT / THHH / THHT / THTH / THTT / TTHH / TTHT / TTTH / TTTT
Given the same reasoning as in your question, we would expect that for a coin flipped with equal chance of outcomes, we would have 2 Heads and 2 Tails after each flip. In reality, only 6 of the possible 16 cases have this configuration.
This same principle can be applied to your original question. I won’t do the math on it because the total number of possible outcomes is (literally) 10^100 but it works the same way.
Hope this helps.
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