For estimating the probability of an event resulting from a random phenomenon, we have to visualize all the possible outcomes of this phenomenon (experiment). It could be a simple event where the probability space is two dimensional or it could be a complex event (dependent on several other random variables) where probability space is multidimensional. When probability is a function of single random variable we are looking at this random phenomenon with a simple perspective. The probability space here is two dimensional with random variable on X axis and Probability on Y axis. For example when we study the change in Blood Pressure with respect to Weight, the probability of an individual suffering from hypertension will be defined by the following two dimensional space.
We discuss another example with more variables in picture. Here the probability space is multidimensional. For example we study the duration of stay of a patient in ICU (Intensive Care Unit) with respect to his weight, blood pressure, blood sugar and cholesterol. The probability of a longer duration of stay (more than average) will be defined by five dimensional Euclidean space. For ease of graphical representation a three dimensional Euclidean space will look like the following.
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