probability

The difference between real probability and our mind’s idea of of probability is fascinating.

  • If you ask people for 2 random numbers out of 10 they’ll probably give you something like 3 and 7 even though 1 and 10 are just as random.
  • 1, 2, 3, 4, 5, 6, 7 seems unlikely to win the lottery even though it’s just as likely as any other combination.
  • Apple had to develop a smart shuffle for iTunes that made shuffle LESS random so it would seem more random to listeners.
2

Can you tell which plot above is randomly generated?

Being able to determine if something is “truly” random is not just an investigation carried out by forensic accountants, sociologists, and law enforcement. Rather it is an interesting and complicated mathematical problem. Consider the two plots above. You may look at the on the left and see the clumps, the spacing, and think “That can’t be the random plot.” And yet it is. The plot on the left has been randomly generated, while the plot on the right is a scatter plot of glowworm positions on a ceiling.

So here, the clumps actually help indicate randomness. Try thinking of it in another way: imagine you have two students who were asked to flip a coin 100 times for homework. The first student was diligent and flipped accordingly:

THHHTHTTTTHTTHTTTHHTHTTHT
HHHTHTHHTHTTHHTTTTHTTTHTH
TTHHTTTTTTTTHTHHHHHTHTHTH
THTHTHHHHHTHHTTTTTHTTHHTH

The second student was lazy and decided to make up his flips:

HTTHTTHTHHTTHTHTHTTHHTHTT
HTTHHHTTHTTHTHTHTHHTTHTTH
THTHTHTHHHTTHTHTHTHHTHTTT
HTHHTHTHTHTHHTTHTHTHTTHHT

Now while it might seem strange that the first student has long runs, it fits closer to what one would expect if the flip is random. On the other hand, in the second student’s data, there is less than a 0.1% chance that they wouldn’t get a single run longer than four in a row!

The images and coin flip data was found at this article. It takes a closer look at some of these topics and provides some pretty neat historical background.

Russian Words For Probability

Here are some adverbs for probability. I tried to range them from most likely to happen to least likely to happen. Please note, my range is rather subjective.

  • точно - really, absolutely
  • скорее всего - most likely
  • наверняка - certainly, for sure
  • вероятно - probably, very likely
  • наверное - probably
  • может (быть) - maybe
Quantum Math Could Explain Irrational Reasoning

by Gabriel Popkin, Inside Science

Quantum theory, developed about a century ago to explain the puzzling behavior of elementary particles, could also help explain seemingly irrational aspects of human reasoning.

The mathematics behind this highly successful physics theory has now provided a way to explain why people respond differently to survey questions depending on the questions’ ordering, scientists report June 16 in the Proceedings of the National Academy of Sciences.

Human reasoning is notoriously fickle, inconsistent and full of seemingly obvious fallacies. A prime example of such apparently irrational decision-making is the “order effect”: Researchers routinely find that the sequence in which they ask survey questions affects how people respond to them. In a 1997 Gallup poll, for instance, when surveyors asked people if they thought Bill Clinton was honest and trustworthy, roughly seven percent more respondents answered “yes” if they were first asked whether Al Gore was honest and trustworthy.

Keep reading

I was extremely busy these past 2 days, moving flat is never an easy job… And I am sorry for not posting here often… But a nice paradox just appeared in my head today: BERTRAND’S BOX PARADOX.

It is a classic paradox of elementary probability theory. It was first posed by Joseph Bertrand in his Calcul des probabilités, published in 1889.

There are three boxes:

1.a box containing two gold coins,
2.a box containing two silver coins,
3.a box containing one gold coin and one silver coin.
After choosing a box at random and withdrawing one coin at random, if that happens to be a gold coin, what is the probability that the remaining coin is gold?  Have a great week. 

  • Professor:ok let's do a little experiment. What do you think the probability is, in this 52 person class, that two people have the same birthday?
  • Student:100 percent
  • Professor:no...
  • Student:yes
  • Professor:there are 365 days and only 52 students, how is that 100%?
  • Student:because there are two twins in front of me
  • Professor:shit... Every time