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

Ask yourself a slightly different question. What’s the probability of throwing exactly 25/25?

Turns out it’s only [about 1 in 9](https://www.wolframalpha.com/input?i=50+coin+tosses).

It’s easier to see with smaller numbers. With two coins, there’s four ways they can fall: HH, HT, TH, TT. Half the time, you’ll see an even 1/1 split. With four coins, you have sixteen results, of which six are even 2/2 splits, for an overall 3/8 (37.5%) probability:

HHHH, HHHT, HHTH, HHTT,
HTHH, HTHT, HTTH, HTTT,
THHH, THHT, THTH, THTT,
TTHH, TTHT, TTTH, TTTT

In general, the more coins you flip, the less likely you’ll get an exact 50/50 split.

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