Probability Model
A probability model is a mathematical representation used to describe the outcomes of a random experiment or event
A probability model is a mathematical representation used to describe the outcomes of a random experiment or event. It consists of two main components: a sample space and a probability function.
The sample space is the set of all possible outcomes of the experiment. For example, if we flip a fair coin, the sample space would be {heads, tails}. If we roll a fair six-sided die, the sample space would be {1, 2, 3, 4, 5, 6}.
The probability function assigns a probability to each outcome in the sample space. It represents how likely each outcome is to occur. The probability of an outcome is always a number between 0 and 1, where 0 represents an event that cannot occur and 1 represents an event that is certain to occur. The sum of all probabilities in the sample space must add up to 1.
For example, if the coin is fair, the probability of getting heads or tails would be 1/2 each, since they are equally likely. Similarly, if we roll a fair six-sided die, the probability of getting any particular number (say, 3) would be 1/6, as there are six equally likely outcomes.
Probability models can be used to analyze and predict the likelihood of various events and outcomes. They are fundamental tools in statistics and probability theory, and are widely used in many fields such as finance, engineering, and biology.
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