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Probability - CMA

Some Useful Terms in Probability

Have you noticed that we constantly use probability in real life and general conversations? While describing the probability of something happening, people may use a lot of different words such as “chance,” “odds,” or even “luck.” These words allow them to explain what they are talking about. Similarly, mathematics also has a few probability terms and definitions that help describe what is being talked about.

probability terms and definitions

Probability Terms and Definitions

It helps to list the various probability terms and definitions used before going in-depth. Hence, you will always understand what is being said, and can always refer back to the list for quick reference and revision. Here are a few important terms in probability, broken down to explain what they really mean.

  1. Probability: The chance of an event out of all possibilities occurring. For example, the probability of obtaining a king from a deck of cards is 4/52, or 1/13.
  2. Experiment: The process of obtaining a possible result. For example, tossing a coin is an experiment, the process through which you can obtain either heads or tails.
  3. Sample Space: All the possibilities together form the sample space. If choosing a single digit number, all the numbers from 0-9 together form the sample space for this experiment.
  4. Event: A particular result or set of results amongst the possibilities in the sample space: For example, obtaining 3 from a die or obtaining a sum of 14 with a pair of dice.

Formula and Usage of Probability

Through the knowledge of these basic probability terms and definitions, a few formulas can be formed. This allows basic calculations and judgments on probability.

Probability = Possibility of an event occurring /  Sum of all possibilities

Here’s a classic worked example:

Player 1 and 2 are playing a game with dice. Player 1 wins if the first die rolls 5 or 6. What is the probability of Player 2 winning?

The probability of Player 2 winning = Probability of Player 2 winning / Probability of either winning

= 4/6

= 2/3

=0.33

Here, the probability of one single event is divided by the sum of the entire sample space to calculate the probability. The rolling of the die hence becomes the experiment, as this is the process through which the results are reached.

Further Probability Terms and Definitions

Through the usage of the basic probability terms and definitions seen above, more specific concepts can be described that allow you to cover a broader number of possibilities and areas. Here are just a few examples to give to hint upon the same:

Events can be dependent or independent. Independent events have no impact on each other’s results. Dependent events, as the name suggests, involve one event whose results can change depending on the previous one.

For example, the probability of a team winning a cricket match can be changed or impacted by the probability of winning the toss and choosing the innings.

You can read more about independent events here.

Experiments can be random or deterministic. Deterministic experiments have only one predefined result, while random experiments have multiple possibilities. A special type of random experiment is the Bernoulli trial, which can have only one of two outcomes. A coin toss, for example, is a Bernoulli trial. These have special formulas that can provide you with further useful information.

Of course, you are not very likely to encounter deterministic experiments in the study and practice of probability. However, it is helpful to be aware of the typical probability terms and definitions used in order to understand the subject further as well as demonstrate your knowledge in the future.

For further reading, you can find out more about Bernoulli trials by clicking on this link. 

Solved Example on Useful Terms in Probability

Q. What is the definition of Events?

Answer: A particular result or set of results amongst the possibilities in the sample space: For example, obtaining 3 from a die or obtaining a sum of 14 with a pair of dice.

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