Conditional Probability
المؤلف:
Papoulis, A.
المصدر:
"Conditional Probabilities and Independent Sets." §2-3 in Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill
الجزء والصفحة:
pp. 33-45
8-3-2021
2011
Conditional Probability
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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