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.
​
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.
​
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
In order to answer this question, we need a better understanding of what the study of probability actually *is*. There is no magic force in the universe that is watching you flip coins and making sure that, at the end of the test, the results will equal 50/50. When you flip a single coin once, there are two possible outcomes, either heads or tails; it will not divide into half-heads and half-tails.
So what, exactly, does probability *mean*? Or to put it another way, what is it *useful* for? What is it actually *measuring*?
Probability only really *means anything* when you are dealing with a large number of tests. What it “promises” is that, the *more* tests you have, the *closer* the “real” values will align with the “expected” values. That’s what probability actually *is* – the distribution of results that the real values *approach* as the number of tests approaches infinity. The way it is typically measured is by performing a very large number of tests and examining the distribution of results.
Probability cannot tell you what will happen in any individual test, since any of the possible outcomes can happen. If you get a low-probability outcome, probability has not “failed” – you just happened to get one of the outcomes that we know must happen *sometimes*, just less frequently than the common outcome.
What it *can* tell you with a high degree of certainty is what will happen if you perform a large number of tests. It is therefore most useful in situations involving large numbers.
For example, people who make plans involving entire populations, such as politicians, economists, or epidemiologists often use statistics to predict the outcome of their decisions. They cannot predict the behavior of any one individual within the population, but if their numbers are accurate, the *overall* outcome on the entire population could be extremely predictable.
Latest Answers