Probability Theory

If you are like me, you were explained the idea of probability at school with cases such as tossing coins, throwing dice, picking cards from a deck, playing roulette, drawing colored balls from containers and so on. You can read many such examples in different tutorials on the web, as well. While there is generally nothing incorrect about them, they may give the idea that this is all that "probability theory" is concerned with. A pretty uninteresting application of simple maths to some unrealistic and boring "random experiments" that do not really interest anyone but geeks. Of course, perhaps you want to earn good marks for automatic answers to little questions such as "what is the probability of scoring more than 4 but less than 10 using two dice". It seems just about as impressing and challenging as doing quadratic equations for fun.

What they typically don't teach you is that probability theory captures what you - and everybody else - have been practicing for since you were born for better or worse, without even noticing. All kinds of thinking and decision making rely on probabilities that we assign to different propositions:

• Whenever you see something (like the picture in the description of this lens), you subconsciously determine the probabilities of viewing different scenes. You decide what the picture presents and whether it is "credible" or not;
• Before you cross a street, you subconsciously determine the probability of being overrun by a car and crossing safely;
• Whenever you buy something, you determine the probability of getting what you desire for your cash;
• Police investigators find who dun it based on probabilities of seeing different kinds of criminal evidence;
• Bad guys ponder how to minimize the probability of getting caught;
• Scientists look for which theory is more probable than others for explaining an observed phenomenon;
• Businessmen find out which deals are more likely to be profitable;
• Politicians find out which public announcements are more likely to convince voters;
• and so on, and so forth.

The most important thing to note is that we are almost never 100% sure about anything. We can be rather certain or rather hesitating about various matters, but we can seldom earnestly declare: "I know it for sure" or "I know it's not at all possible" - except maybe when banal and boring stuff is concerned. To phrase it a bit differently, whenever we need to reason and select alternatives, there is some uncertainty.

Real applied probability theory systematically improves our common thinking and decisions

• It's about arriving at the best conclusions based on whatever we already understand and know;
• It's about not getting confused or deceived;
• It's also about realizing how to act to become better informed about things that matter.

The idea of probability is rather difficult to comprehend, though mathematically very basic. A very small part of it is about tossing dice and drawing balls from urns at school.

Visit my blog to read the full series of articles without distracting clutter.

Thank you!