Basic Probability and Statistics

What is Basic Probability?

With applications 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.

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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