Introduction
A lot of people are familiar with the concept of probability but do not understand it. This short article will end with an illustration showing why you don’t understand probability; but I will start with a quick explanation of probability for those new to the concept.
Heads or Tails?
For a lot of us, this was our introduction to probability. Intuitively you knew that a coin would not land on heads every time. So, what is the chance; there are two sides, the coin is shaped uniformly. Instinctively we all assume it is 50-50, equal chance for heads or tails, and you would be correct, this isn’t a trick.
A fair coin has a 50% (1/2) chance to land on either side, we ignore it landing on its edge because that is so rare that the probability is close to 0. You can now apply this to dice, there are 6 sides so getting a particular number, say 5 is a 1/6 chance.
You now understand the basics, lets touch on some common misconceptions
Misconceptions
I have seen quite a few, but I will focus on the ones that are made day to day. The funniest error in logic is when someone is asked a question like “what is the probability of rain today?” and they say “50-50, either it rains or it doesn’t”. If only probability was that simple, you would never need a calculator.
The second misconception is how people determine if an investment or deal is a “sure thing”. They see a success rate of 90% and feel this is guaranteed and can not fail. The human brain does a funny thing of ignoring the 10% as inconsequential.
How bad this backfires is determined by the risk attached, if you lose your profit and get your money back, sure u can try it. But if the 10% is the chance of losing all your money, it is best to gather more data before entering into the deal.
The Monty Hall Problem
Now it is time to test how well you understand probability. The background is simple, you are on a TV show and there are 3 doors. Behind one door is a brand-new Mercedes Benz, and the other two doors have goats behind them.
You are given the choice to pick a door at random. You pick one, now the TV host opens one of the doors you did not pick to reveal a goat. He then asks you a question, “Do you want to change the door you picked?”. What is your answer? Try to decide on your answer before you continue reading.
Picking the car when there were 3 doors is a 1 in 3 chance (1/3), so you had a 33% chance of getting the car. After he reveals the goat, you are left with two doors, now you have a 1 in 2 (50%) chance that there is a car behind each door. The correct decision here is to change the door you initially picked; it is decision with the highest chance of success.
Conclusion
The Monty Hall problem simply shows how some of our decisions are driven by emotion and not by an urge to pick the best option. People become emotionally attached to a choice and refuse to let go even if the data says otherwise. Did the Monty Hall problem beat you? Feel free to let me know
My Boat Stopped In Transit
Yes Olumide, it beat me, but I still don’t see how. After one door reveals a goat, the probability of either of the 2 remaining doors containing the car rises to 50% each. Thus how is changing my choice a better decision than sticking to the old one?
It is better because you had a high chance of initially picking the goat 2/3, so swapping increases your odds now of getting the car. Best way to visualize it, if there were 100 doors with 99 goats and 1 car, and u picked a door. Then he opened 98 doors to show u all goats, I’m 100% sure you are switching that choice. With just 3 doors, the odds are smaller but still better