By accident, I came across a listing of ‘Thinking Traps’ recently and one of these caught my eye, ‘The Coincidence Trap: We Suck At Probabilities’.
An example is given of the Birthday Problem and it’s an interesting case where the results seem at odds with everyday intuition and gut feel.
In probability theory, the birthday problem, or birthday paradox pertains to the probability that in a set of randomly chosen people some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (including February 29 births). But perhaps counter-intuitively, 99% probability is reached with just 57 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (except February 29) is equally probable for a birthday.
The mathematics behind this problem led to a well-known cryptographic attack called the birthday attack.
The moral from this is that sometimes your gut feel can be way out and you need (at least) to be aware of this. However improving and developing your intuition would be a better way forward as ‘following your gut feel’ is a common and powerful adage.
An unusual but tantalising example of this is the idea that luck can be enhanced by following some Luck Principles (themselves extracted from the experiences of a selection of lucky and unlucky people) and two of these are: Listen To Hunches and Boost Your Intuition.
Lucky people do many different things to enhance their intuition. Some simply clear their minds, while others invest time in more formal forms of meditation. Some go to a quiet place or stop thinking about a problem and return to it at a later date.
Sleeping on problems is an excellent way of developing solutions (there even seems evidence for this) and presumably taking a course on statistical thinking is another way of improving matters!