A closer look at random experiments
The concept of random experiments is not as clear as you might think. Uncollapse for some examples highlighting some of the finer subtleties.
Clearly it is not possible to predict the weather with accuracy. One conclusion is that there is a random element involved, which is also reflected in the expression that it "rains tomorrow with a likelihood of ", or so.
However, just because an outcome seems to be random, it could in fact be totally predictable if we would understand the underlying process better and know all the initial conditions. This in fact is the case for the weather, which is a deterministic chaotic system.
The weather appears random, but only because the weather system is highly sensitive to fluctuations of its parameters such as air pressure or temperature everywhere on the planet. Small fluctuations or measurement errors at one location might be enough to turn a sunny day into a rainy day ("butterfly effect"), and consequently it becomes very difficult to make an accurate weather forecast.
We all agree that flipping a coin is a random process - it is simply not possible to predict if head or tail will occur. But this is not so at all, claims Professor Persi Diaconis from Stanford University. He shows that the actual flip of the coin is a deterministic process, governed by Newtons law. Randomness is introduced by our inability to repeatedly throw a coin in exactly the same way. Checkout the article below (uncollapse), and you can also watch the following video clip: video clip.
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DAVID KERSTENBAUM, February 24, 2004
Flipping a coin may not be the fairest way to settle disputes. About a decade ago, statistician Persi Diaconis started to wonder if the outcome of a coin flip really is just a matter of chance. He had Harvard University engineers build him a mechanical coin flipper. Diaconis, now at Stanford University, found that if a coin is launched exactly the same way, it lands exactly the same way.
The randomness in a coin toss, it appears, is introduced by sloppy humans. Each human-generated flip has a different height and speed, and is caught at a different angle, giving different outcomes.
But using high speed cameras and equations, Diaconis and colleagues have now found that even though humans are largely unpredictable coin flippers, there's still a bias built in: If a coin starts out heads, it ends up heads when caught more often than it does tails.
Note: In football's inaugural kick-off coin toss, the coin is not caught but allowed to bounce on the ground. That introduces an extra complication, one mathematicians have yet to sort out.
So, does "real" randomness exist at all? Quantum physics, that is, the theory that explains the behaviour and interactions of the very small particles (atoms and electrons, and smaller) turns out to be governed by true randomness (see for example the "double-slit-experiment"). Again, one could argue that the unpredictability is due to some hidden, still unknown rules underlying the behaviour in the quantum realm. However, most experts in the field seem to agree that this is not the case. Real randomness seems to exists.
If true randomness exists is also of huge interest from a philosophical point of view, in particular if we ask ourselves to what degree our own actions are fully determined at birth or even earlier ( fate, free will).
In any case, for our purpose we are satisfied that certain experiments exist whose outcomes are for some reason unpredictable, but a probability to occur can be assigned to each of its outcomes in a reliable way using the long-run relative frequency.