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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%
Hi ganeshie8, I've drawn a tree diagram of probabilities, but am having some trouble making sense of the question...
80% of available pieces are real and 20% are fake : |dw:1437554345284:dw|
nice font btw
The probability for critic identifying "fake piece" as "fake" is 90% The probability for critic identifying "real piece" as "real" is 50% |dw:1437554570150:dw|
Yep, thats what I did too
fill in the probabilities on other braches |dw:1437554742335:dw|
we're given that the critic identifies the piece as fake, so highlight those branches : |dw:1437554822270:dw|
p("real" | "c-fake") = P("real" and "c-fake") / P("c-fake")
= 0.8*0.5 / (0.8*0.5 + 0.2*0.9)
why do you divide those two?
because we know that the critic identified the piece as fake, the sample space reduces to only those two branches that end with "c-fake"
okay so out of all the times that he says its fake, we are looking at the times its actually real
np you could work this using bayee's theorem formula but i feel tree diagrams are a great way to visualize/work these problems involving conditional probability
whats bayee's theorem? If its quick to explain that would be great, otherwise ill wikipedia it!
check this https://www.khanacademy.org/computing/computer-science/cryptography/random-algorithms-probability/v/bayes-theorem-visualized