I know, 50/50 heads tails right? But help me understand the next step – each coin flip has a 50/50 shot of heads or tails. What I don’t understand is how the likelihood of the next flip doesn’t change. For example if I flipped a coin 10 times and every time it flipped heads, the next flip would be 50/50 tails. Wouldn’t the likelihood of flipping a coin 11 times and having it be heads every time be really low? 0.5^11 = 0.048%?
Here’s the origin of the question. I was at a roulette table and the guy said “it’s been black the last 8 rolls, the next one has to be red.” At first I thought, the next roll will be ~47% black, ~47 red, ~6% 0 or 00 you fucking imbecile. Then I thought to myself, what are the chances that there are no red rolls in 9 rolls, which is well below 1%.
Am I the imbecile?
In: 215
You’re conflating a single event with a series of events.
When looking at a individual event, yes…. the NEXT flip has a 50/50 chance. It doesn’t matter what comes before. They are not related in any way.
A specific series of events that lead up that that flip might be less likely.
To expand, let’s say we are going to flip 3 total times.
Each individual flip has a 50/50 chance.
But with 3 flips, there are 8 total potential sequences… each *sequence* has a 12.5% chance of occurring.
H H H
H H T
H T H
H T T
T H H
T H T
T T H
T T T
So, yeah, you have a 12.5% chance of getting 3 heads in a row…. but you ALSO have a 12.5% chance of gettting two heads in a row followed by a tails. and ALSO have a 12.5% chance of getting Tails, Heads, Tails. Each sequence has the same likelihood of happening.
… and you can think of a ‘single flip’ as a ‘sequence’ of one… where there are only two options – heads or tails.
A lot of times, with probabilities, it helps to literally write out all the options… then you start seeing a pattern and can extrapolate to bigger numbers.
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