For example, when I flip a coin, I have a 1/2 chance of getting head, and the same chance at getting tails. With that theory, if I toss a coin 50 times, I should get 25 heads, and 25 tails.
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However, I did 3 rounds of 50 coin flips, with results of:
1. 28 heads, 22 tails
2. 27 heads, 23 tails
3. 27 heads, 23 tails.
I assumed that perhaps the coins weren’t “true”. Maybe the sides are waited different, maybe I tossed with different height/force each time. So I went virtual, and switched to having a computer roll a dice.
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I should have a 1/6 chance at rolling a number between 1-6. So 60 rolls, should have each number come up 10 times. But in practice my results were:
1. 14
2. 9
3. 8
4. 13
5. 6
6. 10
So how come practice/reality, doesn’t align with theory, even when we take human error out of the equation?
In: 34
The best way to look at this is to break it down. Let us start with the computer one. Computers use something called “pseudo random number generation.” This is like asking a kid to randomly pick numbers. Sometimes he kid might try to make sure there is no pattern and other times the kid might say “5” every time. Think of that kid’s brain as what’s called a “seed.” Computers will use a seed as a basis of an algorithm (math equation) to generate a “random” number. You can use all kinds of things as seeds such as time, other equations, constant numbers, etc. Every seed will produce a type of pattern in the results. People can mitigate this with more complex algorithms and seed generation. However, for most “random” generators you find online, they will have a very simplistic generator that will be “biased” towards certain outputs as the computer can’t “really” pick a random number.
Now if we look at the coin toss we can break down “probability” and “statistical likelihood.” If you flip a coin and it lands on Heads (H) the next flip has (ideally) a 50/50 probability to be H/T and a 50/50 statistical likelihood of H/T. If you flip it 10 times, the probability that each individual flip is H is exactly 50%. However, the “likelihood” that EVERY flip results in heads is 1/1024 (possible outcomes ^ attempts = 2^10 = 1024). So we can approximate that if you flipped that coin in sets of 10 for ever and ever and never stopped, on average you would have a full 10 H set every 1024 sets of 10. That said, even if you flipped it 9 times and all 9 were H, there is a probability and likelihood of 50% that the 10th flip is also H but there is only a 1/1024 chance that all 9 flips before AND the 10th flip were/are H.
In other words, the likelihood of you getting hit by lightning once in your life are 1 in 15300. However, every thunderstorm you’re in you either do or do not get hit by lightning. 50/50 for the binary result of “did it happen” but the statistical likelihood is improbably small for “will every charged particle between you and the sky form the perfect discharge path for the lightning bolt to hit you.”
Statistical likelihood cares about every step of the process from the start to the end, and probability only cares about the next result as if it were the first result. If you flipped your coins until the end of time you would get almost an exact 50% H and 50% T distribution (assuming it was a perfect coin and perfectly repeatable flip).
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