Thread: Proof 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

Originally Posted by rpatel

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

Are you looking for the proof of this theorem? i wasnt sure



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

are bayes theorem and theorem of total probability the same thing ?

I though total probability theorem had something to do with 'paritions'.

Originally Posted by rpatel

are bayes theorem and theorem of total probability the same thing ?

I though total probability theorem had something to do with 'paritions'.

They are different things

in the website scroll down to Law of total probability

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