Probability (Part 1/2)

I have never really understood probability, since most of the time it defies common sense.  There is a large gap between the statistical probability of an event versus the actual result.

Take, for example, the most basic probability test - flipping a coin.  There is a 50/50 chance of it landing on either heads or tails.  If you flip a coin once, the result will either be heads or tails, not both, not neither.  Even though there are two possible outcomes, there is only 1 result.

Generally people like to average probabilities, attempting to get one single total result from the possible outcomes.  If I had a hat full of dollar bills of varying value, and decided to pick one randomly and give it to you, the probabilities could be as follows:  There is a 20% chance of picking a $10 bill, a 20% chance of picking a $5, and a 60% chance of picking a $1.  If you were to perform some calculations, you could say on average you would receive about $3.60.  There is no $3.60 bill, however, and this outcome is impossible.

This concept also applies to many things in real life such as weather.  If there is a 30% chance of rain, will it rain 30% of the time and not rain for the remaining 70%?  It could, although that is not the only result.  It could rain for half of the day, or it might not rain at all.

This averaging of possibilities is what common sense tells us, and is what most people tend to think.  However, I'll bet you that if you flip a coin it won't land on its side.