Hi

My question is

State and prove the theorem of total probability ?

I tried looking for this proof in my textbook but i can't seem to find it anywhere

any help is appreichated

thanks

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- Dec 22nd 2009, 01:37 PMrpatelProof of total probability theorem
Hi

My question is

State and prove the theorem of total probability ?

I tried looking for this proof in my textbook but i can't seem to find it anywhere

any help is appreichated

thanks - Dec 22nd 2009, 01:56 PMfirebio
Are you looking for the proof of this theorem? i wasnt sure

http://mathworld.wolfram.com/images/...dEquation1.gif

I am not sure if i can post external links on this website...

Check out

Baye's Theorem explained with proof | TutorVista

it has a proof of this theorem - Dec 22nd 2009, 03:39 PMrpatel
are bayes theorem and theorem of total probability the same thing ?

I though total probability theorem had something to do with 'paritions'. - Dec 22nd 2009, 03:44 PMfirebio
- Dec 23rd 2009, 01:25 AMMoo
Hello,

Law of total probability :

For a partition of , the probability space, for any event B (and for higher levels, considering the measured space , for any ...), we have :

and the proof.... :

So

But the last union is a disjoint union : (very easy to prove)

Thus the probability of the union is just the sum of the probabilities :

Then just use the formula