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
You’re mixing what’s called “conditional probability” (the probability of something happening *given that something else happened*) with the single-event probability.
The probability of red or black on *any* single spin is 50%. This is always true (on a fair wheel) regardless of prior results. The ball and wheel have no “memory”, nothing changes between spins. The odds of red on the next spin don’t drop if the prior spin was red, it’s still 50%.
But that is NOT the same as the probability of two reds in a row. That requires that the first spin be red (50% chance) *and* the next spin be red (50% chance). The joint probability is 25%. The probability of red on the second spin didn’t drop, it’s the probability of the overall outcome of two spins that is lower (because you’re specifying one outcome out of a possible four, rather than one in two).
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