HELP WITH PROBABILITY! Question posted below :)

Question

anonymous · Answer

An art critic is surveying a gallery to find a piece that he would like to buy. The piece however has been copied by numerous people throughout the years such that 20% of the paintings in circulation are fake. the critic correctly identifies a fake as being fake 90% of the time; but only correctly identifies a real piece as being real half the time. The critic finds the painting and believes is is a fake. 

What is the probability that the painting is real?

40%
50%
69%
80%

anonymous · Answer

Hi ganeshie8, I've drawn a tree diagram of probabilities, but am having some trouble making sense of the question...

ganeshie8 · Answer

80% of available pieces are real and 20% are fake :

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