Why do you think 20% of the players score 80% of the goals? The populations of the three main Spanish cities are, approximately:
- Madrid: 3,332,000
- Barcelona: 1,660,000
- Valencia: 808,000
The three most common surnames in Spain are:
- García: 1,450,000
- Rodríguez: 926,000
- González: 922,000
How do these lists confirm or question what was seen last week? And what do you think will happen over time with regard to surnames: will there be more and more Garcías or will their proportion decrease?
In a report from the RAE, the following ten most used words in Spanish appear:
- From: 9,999,518
- The: 6,277,560
- What: 4,681,839
- El: 4,569,652
- At: 4,234,281
- Y: 4,180,279
- To: 3,260,939
- The: 2,618,657
- Se: 2,022,514
- From: 1,857,225
How do you interpret the numbers that accompany each word? What conclusions do you draw from the list?
Regarding the anecdote of Hill’s students who cheated when they were asked to toss a coin 200 times and record the results, our recovered commentator Luca Tanganelli raises, after a long absence, an interesting question: “the real question is whether one of Hill’s lazy students might have gone unnoticed. “Can you do randomness consciously?”
Can you think of any way to “do chance” without using dice, coins or other devices? Sometimes readers complain that I propose some problems that are too difficult, and in this case I have to admit that I have gone too far, since calculating the probability that when tossing a coin 200 times, 6 heads or 6 tails will come up at some point followed is frankly complicated; but, since I proposed it and someone may have tried to solve it, here is Bretos Bursó’s solution:
“The probability that in 200 tosses of a coin there will be 6 consecutive coin tosses is not easy to calculate. I estimated it with simulations and saw that it is approximately 0.965. Later I turned to Online Encyclopedia of Integer Sequences (OEIS) and I know how to express it: it is 1-a/2^(199), where to is a 59-digit number, the (200.5) component of triangle A126198 in the OEIS. Since it doesn’t cost me anything to copy and paste, to It is specifically 27870089767928389254900226744638057842249669417272614584184 (if Mathematica doesn’t lie to me).
The probability is then 0.96531280, rounded to eight decimal places. To put it as an exact fraction, this is:
96949866545195843564510102428242905427356478434265475383313/
100433627766186892221372630771322662657637687111424552206336
If eight decimals are not enough, you can always carry out the division.
The 80/20 rule
At the end of the 19th century, the Italian economist and philosopher Vilfredo Pareto enunciated the principle that bears his name, based on a series of observations whose results showed the surprising repetition of a pattern of proportionality. Pareto observed that 80% of the land in Italy was owned by only 20% of the population, and that 20% of the plants in his garden produced 80% of the fruit.
Another would have thought that this was a curious coincidence, but Pareto examined a large number of phenomena and came to the conclusion that, in many different fields, 80% of the effects came from 20% of the causes. That is why its principle is also known as the 80/20 rule or the principle of few factors. Some examples:
20% of the players score 80% of the points (you can check this – or not – by consulting the statistics of your favorite sport).
80% of a company’s profits come from 20% of its customers.
80% of software failures are generated by 20% of the software’s code, while the other 80% of the code generates only 20% of the failures.
A humorous variant of this last statement circulates among computer scientists, known as the ninety-ninety rule:
“The first 90% of the code takes up 90% of the development time, and the remaining 10% of the code takes up the other 90% of the development time.”
#Pareto #principle #players #score #goals