Probability

A measurable quantity describing the frequency of occurrence of a given event.

The classic demonstration of probability is the "balls in the bag" experiment favored by school teachers around the planet.  The script runs like this:

A bag contains 50 red balls, 40 white ones and 10 black ones.  James puts his hand in the bag and picks a ball, what is the probability that it is black (the answer is 0.1).

Subjective and Objective Probability

An event is anything that happens such as a piece of string exceeding a given length or a particular horse winning a race.  It is important to distinguish between objective and subjective probability.  Objective probability is based on observations.  For example, if you have 25 years of data for rainfall in June, it is possible to make a statement such as "One in five days will be wet" based on an analytical process.  Without the data, any statement on the weather is just a subjective estimate.  However, the "data" may be people's experience of the weather.  With infrequently occurring events, subject probability may be the only form of input available.

Expressing Probability

There are several ways of expressing probability:

Ratio (range 0 to 1)

This is the ratio of the number of successes to the number of trials.  Using the "balls in the bag" example, if James performs the experiment 100 times (replacing the recovered ball after each go) and records 10 black balls, the probability of getting a black one is 10 divided by 100, i.e. 0.1

Percentage (range 0 to 100)

This is the ratio described above multiplied by 100.

Odds

This is the ratio of successful trials to unsuccessful ones.  Keeping with our example, we have 10 successful trials (e.g. 10 black balls) and 90 unsuccessful ones (90 balls which were not black), thus the odds of a black ball are 10/90 e.g. approx.  0.111.

The relationship between ratio and odd is:

The betting industry favors the odds form of notation, sometimes using the term price.  If the odds on a horse are quoted at 9-1, this means that in ten races, the horse will lose nine times and win once. 

Page updated: 17-Dec-2004

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