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By: Neil E. Cotter
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Probability
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Basic probability |
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Law of total probability |
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definition |
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Tool: The
Law of Total Probability states that, given a partition A1, A2,
A3, ..., An of sample space S, the probability of any event B
is given by the sum of the probabilities of B
intersected with each of the Ai:
The Law of Total Probability is often used to find one unknown probability of the intersection of events when all of the other terms (including P(B)) are known.
A Venn diagram illustrates the law of total probability in an intuitively obvious way.
Here, n = 6. It is easy to see that the area of B, which represents P(B), is equal to the areas of the overlaps of B with each of the Ai.