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Probability Grid Method

A probability grid, or lattice diagram, is a table-like structure that displays the outcomes of probabilistic trials. The method associated with probability grids, the probability grid method, is one that many introductory probability courses use to introduce students to deriving sample spaces, sets of outcomes for probabilistic trials. This method has both advantages and disadvantages, and you should consider these pros and cons before deciding whether the probability grid method will be useful for your course.
  1. The Probability Grid

    • The probability grid itself looks much like a table. The columns and rows represent separate types of events. A simple example is a probability grid for the result of tossing a coin and rolling a die at the same time. In this case, the rows can be the results of the coin toss (heads or tails), while the columns can be the results of the die toss (1 to 6). The cells in the grid represent the outcome corresponding to the row and column for that cell. For example, the cell (1,5) may represent the outcome of seeing a "heads" and a "5" on the simultaneous toss of a coin and die.

    Purpose

    • The primary purpose of the probability grid is to display the sample space of a trial. In probability, the sample space contains the complete set of possible outcomes for a trial. For the coin and die example, it is easily seen that the cells show every possible combination for the trial of throwing a coin and die simultaneous. Thus, that probability grid's cells altogether represent the sample space of the trial.

    Advantages

    • The probability grid method is especially useful in both the teaching of probability to new students and in deriving the sample space for trials that involve two actions, such as rolling a die and tossing a coin. The probability grid is intuitively easy to read and derive, making it a useful tool for introductory probability courses. In addition, in many cases creating a probability grid allows you to write the complete sample space much more quickly than exhausting all the trial outcome possibilities one-by-one as a traditional mathematical set (i.e. writing out every possible outcome in words or mathematical language).

    Disadvantages

    • The probability grid method has the disadvantage of only being useful in cases where the trial is one that combines two actions; it cannot be used for trials combining many actions, due to the two-dimensional nature of a grid. Unfortunately, this disadvantage disallows the probability grid method to be useful throughout the study of probability; after introductory probability courses, the probability grid method ceases to be useful.

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