found throughout many aspects of life, an understanding
of basic probability can lead to sound decision making
through simple analysis. Wanting to know how likely it
would be to get hit by lightning and calculating the
chance of rolling a 12 on a pair of dice, are two
examples that can be described through probability.
In its most basic form, probability simply measures the
chance that a particular event will produce a particular
outcome when compared to all possible outcomes of the
event. To describe this concept, we shall use a very
popular example, the rolling of a six sided die.
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A roll of a six sided die will produce a single result
of one, two, three, four, five or six. What if we want
to know the chance, or probability, that a single roll
will produce a result of six? To calculate this, simply
divide the number of ways to roll a four, by the number
of total possible outcomes from the roll. In this case,
we have one way to roll a four and six total possible
outcomes, giving a probability of one in six. This can
also be expressed as a probability of 0.167 which
equates to a 16.7 percent chance.
Now, consider the case of rolling a pair of dice with
results possible from two to twelve. Since there is more
than one way to roll every outcome except two and
twelve, the probability calculation is slightly more
involved. First, we need to determine how many ways each
outcome can occur.
For two and twelve, there is only one possible
combination each that yields these results; both dice
must be one or both dice must be six. The resulting
probability of either of these events is therefore one
in 36 yielding a probability of 0.278, or 2.78 percent.
Every other possible outcome has multiple possibilities.
For example, the outcome of rolling a three has two
possible combinations: die A is a one and die B is a
two, or die A is a two and die B is a one. The
probability of rolling a three is therefore two in 36
for a probability of 0.056, or 5.6 percent.
The field of probability is vast with applications
ranging from gambling theory to signal analysis. Even
the most complex of these problems, however, has a
foundation built on the basic concept described here.
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