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

Your theory is based on 50 flips, with a 50/50 outcome, should be 25 to each side.

However your practice isn’t the same test. You’re doing 50 individual 1/2 tests.

If it’s easier imagine a bag of 50 marbles, 25 are red, 25 are blue.

In your theory, your pulling out the marbles one at a time and marking down the colour, but then you leave the marble. Out of the bag, and at the end you’ll have 50 marbles, 25 are red 25 are blue.

In your practice, you’re pulling out a marble noting if it’s red or blue, and then putting it back in the bag before pulling out a marble and marking if it’s red or blue.

It’s not the same test.

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