What Countable sample space is
In statistics, a countable sample space is a set of elements (also known as sample points or outcomes) that can be counted, or enumerated, in a finite or infinite number of steps. A countable sample space is often used to represent the possible outcomes of a random experiment.
The steps for counting a countable sample space are as follows:
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Identify all possible outcomes: The first step is to identify all the possible outcomes of the random experiment. This will form the elements of the sample space.
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Number the elements: The second step is to number the elements of the sample space. This can be done either by assigning numbers to each element in an order, or by assigning a distinct number to each element.
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Count the elements: The third step is to count the elements of the sample space. This can be done either by counting the elements one-by-one, or by counting the elements in groups.
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Determine the sample space size: The fourth step is to determine the size of the sample space, which is the total number of elements in the sample space. This can be done either by counting the elements one-by-one, or by counting the elements in groups.
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Record the results: The fifth step is to record the results of the count, which will provide a record of the sample space size. This can be done either by writing the results down on paper, or by using a spreadsheet or other software.
Examples
- A sample space containing the outcomes of flipping a coin three times.
- A sample space containing the outcomes of rolling a die two times.
- A sample space containing the outcomes of drawing two cards from a standard deck of 52 cards.
- A sample space containing the outcomes of spinning a spinner with six equal sections.