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?
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When you pick a number with a 10% chance, the chances of picking the second number, for each number, is not 10% anymore, it’s 10% x 10% which makes it a 1% chance. To ELY5, you pick 1 and then you have 10 choices for the second number, you pick 2 and then 10 choices for the second number… We have 10 choices for the first number and each choice has 10 choices for the second number. 10×10=100. So the chances of picking a 7 and then any number is 1%. Chances of picking a 7 and then a 7? 1%. By picking more numbers, you make more probabilities. Each step you add to pick a number gives you 10 new possibilities per each possibility you had before. So, if you pick a 7, the chances of picking a number between 1-10 is also 1%, however, the chances of picking 7 and 7 again is 1%, but the chances of picking 7 and then any number but 7, is 9%, which is much higher than 1%. (PS: If you want to pick the number 7 a hundred times, the probability of it would be 1 in 10^100)
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