Hello,

I am new here! Nice forum by the way.

So i have a weird proof to solve there that kind of remind this one but its seems that its quite different, after all.

B, C are mutually exclusive.

And i have to proove this:

P(A | B ∪ C) = [ P(B) * P(A | B) / P(B) + P(C) ] + [ P(C) * P(A | C) / P(B) + P(C) ]

I have tried load of things, but mostly i am doing cycles around. I am definatelly missing some keypoint ?

Shoud i try proove it by taking the long part and reach P(A | B ∪ C) , or should i take small part reach the big one?

Honestly i have tryed both way and nothing absolutely nothing.

On my best attempt i reached this point (by taking the long part trying to reach the 1st part):

P(A∩B) + P(A∩C) / P(B) + P(C) and i cant continue from this point. i mean that if "+" was like "or" i could probably say that

P(A∩B) + P(A∩C) / P(B) + P(C) = P(A∩(B∪C)) / P(B) +P(C) and finish it here (but its wrong)...

Any ideas there ?