Is tossing of a coin deterministic experimemt?

I think a way to understand this is to compare to another deterministic transformation: the baker's map. If we always choose the same initial point in the square and apply 30 times the baker's map, the image of that point in the square will always be the same, in this sense, it is perfectly deterministic. But if we have the slightest inaccuracy in the initial position, the position after 30 iterations of the map becomes unpredictable, and has all the appearance of randomness.

Systems where small variations of the initial data implie large or unpredictable variations of the final outcome are common in mathematics. One often cites the butterfly effect in chaos theory to illustrate this. Many non linear hyperbolic systems of mathematical physics have the same behavior.

This is a good question and should always ask questions like this if you want to want scientific answers! Dont get discouraged by one teacher who does not like to be challenged.

To your question: Yes you are right. If you would build a robot that always uses the same force in a vacuum with no wind and the exact same coin the result would always be the same.

HOWEVER: In normal life there are so many small things you can not control that the result seems to be random every time.

So for all purposes of statistic evaluations and computations actually tossing a coin (or rolling a die) will be a random experiment.

One interesting sidenote: Creating random things is REALLY hard to do for a computer! They do exactly the same things every time. Because of this, computers create pseudorandom values that can be exactly reproduced by the computer but seem to be random for the human eye.

I teach my class that tossing a coin is a deterministic experiment.

First though, you need to fully define "tossing of a coin". I also don't fully define this, but essentially I say "repeatedly toss the coin under the same conditions". In these conditions, I include:

• same coin (no loss/gain of mass for this coin)
• same side of the coin always starts up
• same force applied resulting in same rotational velocity, height, etc.
• same external conditions, e.g. no wind, same atmospheric pressure, etc.
• and so on

Since quantum effects are negligible, the coin should end up with the same side up, i.e. it is a deterministic experiment.

Now, when most people talk about "tossing a coin" they don't stipulate that all these experimental conditions have to be the same and thus there is a random experiment. In my class, I point out that it is only random because of our inability to exactly replicate the experiment.

As a fun aside, a colleague in graduate school, who also happened to be a magician, told us that he could toss a coin with a much higher than 50% chance of getting a head. He managed to flip the coin about 10 times and got a head every time.