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## Main Question or Discussion Point

P(S

How do I simplfy the above equation if S

_{1}[itex]\cap[/itex] S_{2}[itex]\cap[/itex] S_{3}| r)How do I simplfy the above equation if S

_{2}and S_{3}are independent of r ?- Thread starter bhathi123
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P(S_{1} [itex]\cap[/itex] S_{2} [itex]\cap[/itex] S_{3} | r)

How do I simplfy the above equation if S_{2} and S_{3} are independent of r ?

How do I simplfy the above equation if S

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Stephen Tashi

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[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]

so

[itex] P(A \cap B | Z) = P( (A|B)|Z) P(B | Z) [/itex]

See if you can make progress by applying those ideas.

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