Do random experiments actually exist? I am studying probability and in most of the books that i have read they mention that for an experiment to be random-- (1)there should be more than 1 possible outcome--(2)even when the experiment is repeated under similar conditions the outcomes must not be predictable.The second point really confuses me...if we take a coin toss for example and we repeat the experiment under totally similar conditions   of gravity,air resistance,apply the same force,etc won't we be able to predict the exact outcome every time and as long as the conditions remain same my intuition tells me that i will get the same outcome every time....so do random experiments exist?and if they do what can be considered as a random experiment?
 A: In classical physics it is true that if you were able to reproduce the initial conditions exactly, the result would be the same.  However, in quantum mechanics it is not. If you measure an observable in a state that is not an eigenstate of that observable, the results you get are not determined.  Such a measurement does constitute a "random experiment" in the sense of probability theory.
This is not just theory: you can buy a device that conducts such experiments to produce random numbers
A: This has nothing to to with mathematics but with physics.
A few years ago I had a discussion with some person who claimed that something is impossible because some process is "random"; this is why I was searching the internet for an answer to your question:
According to the website I found it was not possible to find out if there really are processes that are what you call "random". I think that this still is not possible.
However that website said that there are different "levels" of randomness:
One "level" is: Although the outcome of the experiment is predetermined, it is not possible to predict the outcome. Such experiments definitely exist.
A: There is a long standing question of whether true randomness actually exists.  Sometimes these discussions delve closer to theology than math or physics.  Computers have long been criticized for the low quality of their random number generators.
Radioactive decay, and quantum properties are considered to be random.  They are definitely unknowable.
Chaos theory says that many systems have a high degree of sensitivity to initial conditions.  And so, as we move away from these initial conditions, the future state of the system becomes increasingly difficult to predict.  This means that no matter how good our data is, we will never be able to generate good long-range weather forecasts.  It also suggests that coin flipping, dice rolling and bingo hoppers tend to be good random number generators.
So, while we probably can build a coin flipping machine that flips head every time, it is safe to say that a human who has not practiced his coin flipping will only flip heads 50% of the time.
