Statistics for Decision- Making in Business - Maricopa Community ...

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There is only a .9% chance that the three gang members all come from the presumed gang. The
detective should consider more evidence to narrow down the search results before making
assumptions.
Example 4: A business creates a new system to keep track of client relations, such that
information about the client and a particular orders placed can be accessed by a nonrepeating,
four character or digit number. For instance, KA23 and
AK23 are possible codes. Any code containing only letters
will be reserved for large clients. How many such codes of
non-repeating letters can they make available, and
assuming all such codes will eventually be used up what
percentage of the company‟s clients will be considered
large clients
SOLUTION: There are 26 letters in the alphabet and, of
those, four will comprise a single, large-client code. There
are
different codes without the same
letters being repeated, but where order does matter.
In order to know what percentage (or probability) of the total number of possible codes this
represents, we need to compute the total number of codes that can be formed, where no letter or
number is repeated, but where order does matter. This is precisely what permutations are for.
Since there are 26 letters and 10 numbers, a total of 36 different “symbols” can be selected from.
The number of permutations is
total different codes 1 without the same letters or numbers being repeated, but
where order does matter.
So, the percentage/probability, then, is:
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We conclude that 25% of all clients (the large clients) will have completely alphabetical codes.
1 Notice that the increase in the number of possibilities after increasing the size of the sample space is not
proportional to the increase amount. The growth is actually exponential, not linear.
Statistics for Decision-Making in Business © Milos Podmanik Page 127