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
Depends. Is your coin totally balanced, meaning it still has exactly 1/2 chance on falling either way (and no chance of standing on its edge ?). Then flips are independent from each other, and each flip **still** has the exact same chance to fall on either side. Even it it has previously fallen 100 times consecutively on “heads”.
Now, that’s *only* if the coin is really perfectly balanced, and the toss isn’t rigged (like, by having magnetized the coin, and put a magnet to ensure it always falls on the “good” side. Or calculating the required force, and applying it perfectly, in a way that would physically make it certain that it would fall the expected way.
A series of tosses, supposed to be independent, but showing 100% of result A, 0% of result B, is **possible**, even with a perfectly balanced coin, but diminishes exponentially with extra tosses. With 10 tosses, all “heads” has 1/1024 chance of happening. 16 tosses, all “heads”: 1/65536. The formula is 1/2^x (2 to the power of x), with x being the number of tosses.
So, yeah, it’s very unlikely, but not impossible.
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