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_{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 ?

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- Thread starter bhathi123
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How do I simplfy the above equation if S

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Stephen Tashi

Science Advisor

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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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