Need simple statistics help

[RIGorous1]

AT an art exhibit there are 12 paintings of which 10 are authentic originals. a visitor selects a painting at random and before she decides to buy, she asks the opinion of an expert about the authenticity of the painting. The expert marks the painting REAL or FAKE. He is right 90% of the time with both authentic and non-authentic works.

Make the probability tree...

Part 1 answered

Part 2: IF the expert (possibly incorrectly) marks the painting FAKE, then the visitor returns the painting and chooses another one of the rmaining 11 paintings. What is the probability that her second choice will be an authentic original?

 

[Colt45]

.9

 

[RaynorWolfcastle]

make a tree with each of the leaves representing the following probabilities

Painting is real, expert says real (10/12)*0.9
Painting is fake, expert says real (2/12)*0.1
Painting is real, expert says fake (10/12)*0.1
Painting is fake, expert says fake (2/12)*0.9

 

[RIGorous1]

Originally posted by: RaynorWolfcastle
make a tree with each of the leaves representing the following probabilities

Painting is real, expert says real (10/12)*0.9
Painting is fake, expert says real (2/12)*0.1
Painting is real, expert says fake (10/12)*0.1
Painting is fake, expert says fake (2/12)*0.9

so only 4 branches...
lol I was thinking 2 decision for 12 branches... man I suck. Thanks for the help

 

[RIGorous1]

IF the expert (possibly incorrectly) marks the painting FAKE, then the visitor returns the painting and chooses another one of the rmaining 11 paintings. What is the probability that her second choice will be an authentic original?

 

[RIGorous1]

part 2 posted

 

[RIGorous1]

up

 

[EugeneChien]

.1 x 10/12 x 9/11 + .9 x 2/12 x 10/11

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.1 x 10/12 + .9 x 2/12