|Sep7-12, 10:37 AM||#1|
Simplifying the Conditional probability
P(S1 [itex]\cap[/itex] S2 [itex]\cap[/itex] S3 | r)
How do I simplfy the above equation if S2 and S3 are independent of r ?
|Sep7-12, 11:55 AM||#2|
I've don't recall seeing a book that gives the probability law
[itex] P((X|Y)|Z) = P(X | (Y \cap Z) ) [/itex]
but I think its true. How to argue it depends on whether you are approaching probability as measure theory or something simpler.
You can also apply the usual probability laws with a condition lilke "[itex]| Z[/itex]" tagged onto every term. For example,
[itex] P(A \cap B) = P(A|B) P(B) [/itex]
[itex] P(A \cap B | Z) = P( (A|B)|Z) P(B | Z) [/itex]
See if you can make progress by applying those ideas.
|Similar Threads for: Simplifying the Conditional probability|
|Conditional probability - Probability of spotting a downed airplane (really basic)||Set Theory, Logic, Probability, Statistics||3|
|Probability question; Conditional probability and poisson distribution||Precalculus Mathematics Homework||1|
|[PROBABILITY] Conditional probability for random variable||Calculus & Beyond Homework||13|
|[probability theory] simple question about conditional probability||Precalculus Mathematics Homework||1|
|HELP geometric probability: area of a square and conditional probability||Precalculus Mathematics Homework||4|