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2. Using a Sample Space
A sample space helps you visualize all the possible outcomes of a process. Learn how to create a sample space and use it to calculate probabilities in this lesson.
Lesson Goal (00:14)
The goal of this lesson is to use a sample space to calculate probabilities.
Viewing the Sample Space (01:08)
A sample space is the set of all possible outcomes of a process. For example, when we roll two dice, the sample space is the set of all possible combinations of values on the two dice.
By representing a sample space visually, we can make it easier to identify which possible outcomes correspond to events of interest to us. In our case, we have a 6x6 matrix of outcomes representing the possible values when we roll two dice. We can identify the total number of possible outcomes by calculating the number of items in the matrix.
Calculating Probabilities (02:29)
To calculate the probability of an event, we divide the number of outcomes where that event occurs by the total number of outcomes. A sample space can help us visualize the outcomes where the event of interest occurs.
Calculating the probability of different events allows us to compare how likely these events are. Generally if we’re calculating probabilities for different events, it’s useful to express the probabilities as a decimal, as it’s easier to compare decimal values than fractional values.