If something has a 5% chance of success, and I’ve failed 19 consecutive times, the next time independently still has a 5% chance of success, fairly low, rather than a guaranteed 100% chance of success in view of the previous attempts. How does this relate to updating percentages in light of new evidence, or is that something separate?
In: 6
It’s related to independent and dependent events.
A coin toss is an independent event. Every time I flip a coin, the odds are alway 50% for any given result. It doesn’t matter if the coin has landed a certain way previously; prior results don’t affect subsequent ones because the way a coin lands does not fundamentally alter the coin.
Things like pulling a certain sock color from a drawer are dependent. If I have 19 white socks and one black sock in a drawer, there’s a 5% chance that I pull the black sock on the first try. If I don’t put the first sock I pull back in the drawer for my second choice, now the odds of getting a black sock are up to 1/19 instead of 1/20. Those odds will keep going up as I remove more socks because I’m changing the situation. As there are fewer and fewer socks to pick, it becomes more likely that I get the black one. My future results depend on the changes to the system caused by previous results.
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