why does theoretical probability not align with practice?

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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?

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41 Answers

Anonymous 0 Comments

A lot of answers talking about how probability actually works but that’s honestly kinda irrelevant. Physics will accurately predict the outcome of any coin flip if you have all the necessary information to plug into the equations. Probability is just a way of coming up with a best guess when we don’t have all the necessary information.

But if you place the coin in a very particular way on your hand, flick it in a very particular way with a particular amount of energy, then the coin will follow a particular arc in the air and flip a particular number of times, hit the ground at a particular angle with a particular speed and then perform a particular series of bounces. This means that if you can flip a coin in a consistent way, then it will consistently land the same way too, skewing your results.

Using a computer to randomly generate results won’t guarantee different results every time either though. That’s because computers can’t actually generate truly random numbers. They generate what’s called pseudorandom numbers. There’s a very particular formula they use for generating these numbers that are based on a single starting value known as a seed. You can specify a seed manually, which will result in the exact same outputs every time. If you don’t specify a seed, then the computer will pick its own based on the current time. This gives an illusion of randomness since it’s never the same time twice, but the equations used to generate the numbers aren’t guaranteed an even distribution of the possible outcomes.

In short, nothing is ever actually truly random. Everything can be accurately predicted if you know enough of the variables. And probability is just a framework for making educated guesses when you don’t know all the variables.

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