Statistics: March
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.
General:
Number of searches through 30 days
 1378

Total number of words used in searches
 4268

Number of times safemode was used
 8

Number of words in the database
 7111

Number of times individual words from the database have been used in the searches
Number of words that have been used once
 2215
 31.2%

Number of words that have been used twice
 715
 10.1%

Number of words that have been used three times
 156
 2.2%

Number of words that have been used four times
 31
 0.44%

Number of words that have been used five times
 6
 0.08%

Number of words that haven't been used
 3988
 56.1%

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
 32.9%

Probability a word had been used twice
 9.9%

Probability a word had been used three times
 2.0%

Probability a word had been used four times
 0.3%

Probability a word had been used five times
 0.04%

Probability a word hasn't been used
 54.9%

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
 27
 2.0%

Number of times 2 words was used in search
 9
 0.7%

Number of times 3 words was used in search (default)
 1195
 86.7%

Number of times 4 words was used in search
 106
 7.7%

Number of times 5 words was used in search
 41
 3.0%

The number of times that, within a single search using 25 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 2word
search is 1 in 51 million, and in a 5word search, 1 in 5 million.
Links:
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
Bernoulli Trials.
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