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 version of the theory is a little too strict. Theory actually says that if you flip a coin 50 times, you’ll **usually** get **about** 25 heads and 25 tails. The “usually” part is important. Theory doesn’t say you’ll get exactly 25 of each. The theory also says the more times you flip, the closer to an even split you’ll get. (at least at ELI5 level).

Try going to this site and choosing the 10,000 times option. Watch the “heads” percentage as the coins flip more and more. At first you might see an extreme split, like 70% heads, but as more and more flips happen, the percentage split will get closer and closer to 50/50. I’m up to 200 flips now, and the split is 45% heads and 55% tails. After 300 flips it’s 47%/53%.

https://flip-a-coin-tosser.com/10000-times-flipping/

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