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Date: 16-2-2021
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The conditional probability of an event assuming that has occurred, denoted , equals
(1) |
which can be proven directly using a Venn diagram. Multiplying through, this becomes
(2) |
which can be generalized to
(3) |
Rearranging (1) gives
(4) |
Solving (4) for and plugging in to (1) gives
(5) |
REFERENCES:
Papoulis, A. "Conditional Probabilities and Independent Sets." §2-3 in Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 33-45, 1984.
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