A log is kept of the options and words used for each random search. I wrote a small visual
basic program to analyze everything from the options used to probabilities that certain
words will be used from the past 30 days.
| Number of searches through 30 days
| Total number of words used in searches
| Number of times safemode was used
| Number of words in the database
Number of times individual words from the database have been used in the searches
| Number of words that have been used once
| Number of words that have been used twice
| Number of words that have been used three times
| Number of words that have been used four times
| Number of words that have been used five times
| Number of words that haven't been used
We can compare the results obtained above with that expected from probability theory.
The probability P(x) of an event x
occuring, that has a probability of success p, over n independent trials are called
Bernoulli trials, is given by using the binomial distribution,
In this case, an event would be that a word was used once, the number of trials is 4268
and the probability of success is 1/7111, which is the probability of choosing a single word
from the database of 7111 words. The results are summarized in the table below.
Compare the results with those expected from probability theory.
| Probability a word had been used once
| Probability a word had been used twice
| Probability a word had been used three times
| Probability a word had been used four times
| Probability a word had been used five times
| Probability a word hasn't been used
Comparing the results we obtained with those expected from probability theory, we see that
they agree very well. As more searches are done, it is likely that the differences
between actual results and theory will decrease even further.
Words used 5 times:
individuals, remove, rental, slipped, stored, tells
Words used 4 times:
abilities, advantages, autonomy, base, concerned, contacted, defendants, democratic, distinguished, distributing, distributions, door, firefighters, illustrated, investigator, magic, maintaining, none, overseas, politicians, predictions, relevant, remainder, retiring, sides, singing, specifically, stayed, supporter, transformed, underlying
Frequency of option 'Number of words'
| Number of times 1 word was used in search
| Number of times 2 words was used in search
| Number of times 3 words was used in search (default)
| Number of times 4 words was used in search
| Number of times 5 words was used in search
The number of times that, within a single search using 2-5 words, one word
from the database was repeated within that search:
Zero. It is extremely unlikely that this would occur, as the probability of the same word used in a 2-word
search is 1 in 51 million, and in a 5-word search, 1 in 5 million.
A couple good sites with introductions to probability are:
Basic Probability and
Introduction to Probability.
An introduction to binomial distributions and Bernoulli trials is:
Binomial Distribution and
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