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anonymous

  • one year ago

HELP WITH PROBABILITY! Question posted below :)

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  1. anonymous
    • one year ago
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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%

  2. anonymous
    • one year ago
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    Hi ganeshie8, I've drawn a tree diagram of probabilities, but am having some trouble making sense of the question...

  3. ganeshie8
    • one year ago
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    80% of available pieces are real and 20% are fake : |dw:1437554345284:dw|

  4. anonymous
    • one year ago
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    Yep :)

  5. anonymous
    • one year ago
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    nice font btw

  6. ganeshie8
    • one year ago
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    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|

  7. anonymous
    • one year ago
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    Yep, thats what I did too

  8. ganeshie8
    • one year ago
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    fill in the probabilities on other braches |dw:1437554742335:dw|

  9. anonymous
    • one year ago
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    Yep :)

  10. ganeshie8
    • one year ago
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    we're given that the critic identifies the piece as fake, so highlight those branches : |dw:1437554822270:dw|

  11. anonymous
    • one year ago
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    Okay, yes

  12. ganeshie8
    • one year ago
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    p("real" | "c-fake") = P("real" and "c-fake") / P("c-fake")

  13. ganeshie8
    • one year ago
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    = 0.8*0.5 / (0.8*0.5 + 0.2*0.9)

  14. anonymous
    • one year ago
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    why do you divide those two?

  15. ganeshie8
    • one year ago
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    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"

  16. anonymous
    • one year ago
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    okay so out of all the times that he says its fake, we are looking at the times its actually real

  17. ganeshie8
    • one year ago
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    Exactly!

  18. anonymous
    • one year ago
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    woo hoo

  19. anonymous
    • one year ago
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    Thanks so much for your help @ganeshie8 !!!!!!

  20. ganeshie8
    • one year ago
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    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

  21. anonymous
    • one year ago
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    whats bayee's theorem? If its quick to explain that would be great, otherwise ill wikipedia it!

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