Heads or Tails?

If we flip coin 101 times.
How many heads and tails there will be ?
Over the entire sequence of 101 coin tosses what is the most likely number of lead changes between heads and tails?

People intuition of probability is very poor and usually very inaccurate. Prior to the experiment, just to test out intuition, we were asked how many times we think there would be a change in lead between heads and tails out of 101 tosses. The answers were different; twenty five, six, four, thirty and many others. However, in terms of single most likely outcome the answer is zero.  We been asked to experiment our self’s and see what will be outcome in practise. As you can see from the graphs, the outcome was not zero, yet the number of lead change between heads and tails was not that frequent. Furthermore, overall distribution of heads and tails was very close to 50% heads, 50% tails in both coin tossing experiments. This experiment just proves one more time that people have an illusionary intuition of probability, and that there is a perceptual bias in people’s probability judgment.  

Trail by Toma & Sylwia

Trail by Emma & Claire

Randomness, Probability, and Frequencies

 

Human brain developed to identify patterns promptly, and rely upon those judgments. For example, if our stone-age ancestor’s saw a wolf in the forest, they had to quickly identity possible threat and act accordingly. In case of miscalculation, one died quickly. So, from the evolutionary perspective, the only surviving people today are descendants of the people who were good at making right mental short cuts. However, using heuristics is what usually messes people judgments up. Masculine, bold man with a "Manchester United" t-shirt is not always a football hooligan. People tend to use representative heuristics, when making fast judgments about other individuals.  

Intuition plays a major role in people judgments. But can we rely on our intuition when judging randomness of the events? One the best known randomness miscalculation case is Italian number 53 "nightmare". In Italy's national lottery  number 53 did not popped  for  nearly two years. Some of the people had bet all their life savings hoping that it will appear on the next draw. The mysterious number caused several deaths and bankruptcies.  This example shows us that people have confused perceptions of randomness. I presume that it is a player's dream to have the brain that works like a very advanced calculator then he could always guess the next coming number on the roulette wheel. Unfortunately, human brain is not a computer and we are often misleaded by our illusion of randomness.  

Are there right and wrong decisions?

We need to make decisions every day, weather it is simple ones like, what to have for breakfast, or more complicated ones like, weather to take a job offer. In life we all make some good decisions and some bad decisions. In simple terms decisions with the positive consequences are good and decisions with the negative consequences are bad. 

All people have their individual schema of decision making. Usually is based on their personal experiences. Furthermore, is greatly correlated with their sex, cultural background and religious believes. But we need to keep in mind that decision making is situation specific, and situations are never identical. For example, taking the bus route that always takes you home the quickest, but this particular time there is a car accident on the road and it takes you forever to get home.