Every once in a while I have to convince people that statistics is a counter-intuitive and very difficult discipline. Let me give you some intriguing examples that illustrate you should never trust your intuition to estimate probabilities. Remember this article next time you’re tempted to attribute supernatural powers to somebody that knows personal information about you which seems impossible to guess.
* The Birthday paradox. Imagine you randomly pick people from the street. How many people do you have to bring together so that the probability is more than 50% that two of them have their birth date on the same date?
Answer: only 23.
Explanation at http://en.wikipedia.org/wiki/Birthday_paradox
* Jane is 33 years old, unmarried and very intelligent. She has a degree in philosophy and graduated cum laude. Furthermore, she is a woman with strong believes. As a student she was politically very active; she defended the rights of minorities and participated in anti-war demonstrations.
What do you think is more likely?
A) Jane works at a bank
B) Jane works at a bank and is active in the Women’s Rights Movement
Most people choose the second possibility, but that is wrong: it can never be more likely than the first because it further constraints it (notice the word “and”).
* The Monty Hall problem. Suppose you are on a game show, and you are given the choice of three doors: behind one door is a car; behind the others, nothing. You pick a door, say number 1, and the host, who knows what is behind the doors, opens another door, say number 3, which contains nothing. Then he says “Do you want to pick door number 2?” Is it to your advantage to switch doors?
Answer: yes!
Explanation at http://en.wikipedia.org/wiki/Monty_Hall_problem
* The scoping problem. An US child care organisation successfully went to court to force airline companies to give very young children their own dedicated seats on internal flights. Children had been seriously hurt during near flight accidents being on their mother’s lap and not strapped down. Of course this extra facility/seat costs the parents a bit of extra money, but it would clearly benefit child safety, right? Unfortunately, this decision caused more young children being hurt in the US than before. Why? Because the extra seat costs money and more parents therefore decided to take the car instead of an internal flight; and car accidents happen much more often, so …
* The testing problem. Imagine 1 in 10.000 people is infected with a rare fatal disease and a blood test for this disease gives correct results in 99,99% of the case. What is the probability that you are infected if you test positive for this disease on one such blood test?
Answer: only 50%. This time, I leave the simple math as an exercise to the reader. This is why medical laboratories always test multiple times if a positive comes up.
At this point, it may be appropriate to discuss the probability that some paranormal person guesses (letters) in your first or last name correctly, in particular the modus operandi of the American medium Char comes to mind here. With a bit of searching on the Internet one can easily find lots of statistical information about first names per country, and last names per city or region, e.g. http://www.statbel.fgov.be/figures/d22c_nl.asp
Do you know that 1:4000 Belgium men born after 1975 is named Thomas? Imagine how much you can increase your chances to get it right by combining factual statistical (regional) information with a good sense of readings people’s reactions on your questions.
To summarize, first do the hard math before your intuition tells you something is very unlikely. You’ll be surprised to find that probablities in our interlinked world are much higher than you think.
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