# Probability

### Probability is a measure of the likelihood of an outcome.

## There is No Certainty

There is no order in the universe, everything is random, and change is the only constant. Only probability can determine the likelihood of an outcome, and that outcome is not always guaranteed.

For many centuries it was thought that the universe was completely orderly and that with mathematics anything could be determined. The truth through observation is unfortunately the opposite. Two entities interacting with each other can have their movements mathematically solved and thus they are predictable, but introduce a third body then it becomes unpredictable. Ever heard the saying "**two is company, but three is a crowd**"? A couple is manageable but more people make the interactions far more challenging.

The planned economies of communism started out well but over time crumbled and millions suffered and died. The leaders who created these economies thought that an economy like all other things had underlying mathematics which could be measured and thus the economies could be controlled. Unfortunately this was not true. Many leaders meant well but science and mathematics of the time was based on incomplete studies and flawed.

## Uncertainty Revealed

Scientists studying physics have have looked into the nature of the very small, smaller than atoms. The deeper they go the more the universe reveals its uncertainty. Things do not happen in a predictable manner. At the subatomic level the universe cannot be truly measured (see Schrodinger's Cat below). It is these slight changes that can add up to vast differences as time goes on (see Butterfly Effect below). So while performing the same task over and over, sometimes a different result occurs for no apparent reason - thus the uncertainty.

## Probability Examined

Probability measures the chance of something happening and is commonly observed when throwing a 6-sided dice. The chance of a '5' showing face up is 1 in 6, that is for 6 throws chances are at least one '5' will result. Experimentation will show that for 6 throws (the sample amount) you will likely get between 0 and 2 results. Experimentation with 36 throws (6 x 6) is more likely to get closer to 6 results of '5'. The more times the dice is thrown the accuracy gets better. This is why things are tested, then tested again and again.

Increase the sample amount further and the probability shows itself to be more accurate. Lessen the sample amount and more inaccuracy becomes apparent. Have you ever noticed when something you have done many times sometimes just not turn out as you expect? So check, and re-check your results. The first result may have been 'lucky'.

## Adjusting to an Uncertain World

Having an understanding of uncertainty and probability, and learning skills to cater for them makes life a lot easier. An action done many times will not complete the same way every time. Setting this expectation in your mind allows for acceptance of the various outcomes. Importantly you allow outcomes to have ranges or non-specific criteria instead of precise outcomes, which for the most part are immaterial (engineering excepted).

When precise outcomes are required, the trade off has to be how it is arrived at. Micro-managing a task to critical precision at each step is a waste of time and requires immense effort.

Consider the following Law of Outcomes:

- Short Time;
- Precision;
- Strict Method;
- Pick any two.

It is not possible to have all three.

Choose Precision and a Strict Method, then it will take more time. How often do you see people fight this inevitability.

Choose a Strict Method and a Short Time and there will not be precision. Why? People will be blindly rushing along to method they might not be comfortable with, the results will be sloppy.

Have a think about why Short Time and Precision need a flexible method.