A roulette wheel has a 49% chance (or something i can’t remember but for the sake of this discussion we can just call it 50%) of landing on either black or red. i feel like every time it lands on red, the odds of it landing on red again next spin go down, but also logically i know the odds reset for each spin because the numbers still add up to 50%. Why is it not the former? What is this magic?
In: Mathematics
It isn’t the former because for individual trials, each trial has no impact on the next. Its like flipping a coin. You have a 50/50 shot of heads or tails each flip. If you flip a coin and get heads, and then flip it again and get heads, and then flip it again a minute later, an hour later, a day later, a year later, you have the same 50/50 probability of getting heads.
that is for INDIVIDUAL Trials.
The rules change a bit when you do GROUP trials.
Say you want to know what the probability is of getting heads three times in a row before you even start flipping. (emphasis on making the prediction before you start flipping).
Here the odds are (1/2 * 1/2 * 1/2) = 1/8 or .125. For each individual trail in that group the odds are still 50/50, or 1/2 or 0.5. But when you group them all together the probability does change because now the previous trials impact the next, because you cant get three heads in a row if the first or second trial has already landed tails.
So the probability of getting three heads in a row before you even start flipping is .125, but say you get the first two heads, and now you just need the last flip, that last individual flip is 50/50.
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