Probability is dangerous

Having read books like The Black Swan and Fooled by Randomness (both by Nassim Nicholas Taleb), I'm somewhat terrified by how often we misunderstood probability and randomness. Consider these scenarios.

Probability of getting head tossing a fair coin is 1/2

Probability of tossing 5 heads in a row is 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32

Probability of getting heads after tossing 4 heads in a row is 1/2

The last scenario is where most of us make the mistake of thinking, since there's already 4 heads before this, the chances of getting another head is pretty slim.

This is known as the Gambler's fallacy. The probability is 1/2 because that is probability of getting head tossing a coin. It doesn't matter if we get 4 or 100 heads in a row, the probability remains the same because those events have already occurred and the last coin flip can be viewed as an independent event like the first scenario.

It should be obvious by now that, misconception on randomness and probability can be very dangerous to a gambler but what about the rest of us? With today's ever more complex financial instruments, we are all exposed to certain degree of risk with our investments.

In order to minimize risk, we need to understand probability. Nothing is certain in our lives and not knowing that is dangerous.