Many events in everyday life appear to be random, and the only way we have of predicting them is to use methods of probability. There is no way by which we can know in advance the result of tossing a coin. Indeed, for all examples of deterministic practices, a result could be calculated if we had sufficient data and sufficient skill. For instance, if we knew the exact position where a tossed coin is released and the exact value of its linear and angular momentum, then we have sufficient information to work out whether it will fall heads or tails. However, the necessary precision of the data, and the complexity of the calculation, remove any possibility that we could do so, in the practice of any system. The factors, which must be taken into account are called “hidden variables”, and could never be established with sufficient accuracy.

Moreover it is clear that the tossing of a coin system does not necessarily follow the expected results. Instead of the expected 5 heads and 5 tails, there are 6 tails P = 0.6 and 4 heads P = 0.4. You may think if the experiment was carried out with a larger number of throws, then the result would be more accurate. To show this theory is incorrect, as mentioned earlier, another 10 throws are made:

Probability theory can only analyze those events which can be repeated many times, and in such cases it can make predictions, such as, what is the expected average value of an outcome. For example, before a fair coin is tossed we don’t know if it will land heads or tails, hence we have the probability of the system - P(H) = P(T) = ½. However once the coin is tossed and lands, we witness a change in its probability density function, which answers the rather silly question of whether the odds of a coin landing “heads” remains 1:1 after we have actually seen how it landed. If we choose to use the additional knowledge we have after looking at it, then the probability of a head becomes P = 0 or P = 1, as the case is in Schrödinger’s cat. If we do not, then it remains 1/2. The wave function of the system completely changes once the coin has landed due to the knowledge gained by the flip. When the measurement is made the wave function actually collapses into its final state.

So it is quite clear again. Overall there are 12 Tails and 8 Heads giving probabilities of P(T) = 0.6 and P(H) = 0.4, making it obvious that more throws doesn’t necessarily give a better result.

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