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d) Bayes' Theorem is: P(B|A) · P(A) P(B) P(A|B) = using A as a hypothesis or theorem and B as an observation. A new photography based test is developed that shows if a painting is fake; due to the lack of age of the pigments. The test indicates a painting is fake 95% of the time when the painting really is fake and 10% of the time when the painting is real. The art gallery has 150 painting and predicts that 1 in 7 of its paintings is fake; they use the new test on all of their paintings. i. What is the predicted number of paintings the test will indicate are fake?

d) Bayes' Theorem is: P(B|A) · P(A) P(B) P(A|B) = using A as a hypothesis or theorem and B as an observation. A new photography based test is developed that shows if a painting is fake; due to the lack of age of the pigments. The test indicates a painting is fake 95% of the time when the painting really is fake and 10% of the time when the painting is real. The art gallery has 150 painting and predicts that 1 in 7 of its paintings is fake; they use the new test on all of their paintings. i. What is the predicted number of paintings the test will indicate are fake?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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(d) Bayes' Theorem is: P(B|A) · P(A) Р(B) P(A|B) = using A as a hypothesis or theorem and B as an observation. A new photography based test is developed that shows if a painting is fake; due to the lack of age of the pigments. The test indicates a painting is fake 95% of the time when the painting really is fake and 10% of the time when the painting is real. The art gallery has 150 painting and predicts that 1 in 7 of its paintings is fake; they use the new test on all of their paintings. i. What is the predicted number of paintings the test will indicate are fake? ii. What fraction are correctly detected as fake? iii. What is the Bayesian probability that a painting detected as a fake is actually real? Show your working. iv. If two paintings from an art forger (i.e. both fakes) are tested using this test what are the possible numbers of fakes detected and the probability of each number of fakes? v. How many of the fake paintings would have to be tested to ensure at least a 99.99% chance at one or more of the fake paintings is detected? Show your working.
Transcribed Image Text:(d) Bayes' Theorem is: P(B|A) · P(A) Р(B) P(A|B) = using A as a hypothesis or theorem and B as an observation. A new photography based test is developed that shows if a painting is fake; due to the lack of age of the pigments. The test indicates a painting is fake 95% of the time when the painting really is fake and 10% of the time when the painting is real. The art gallery has 150 painting and predicts that 1 in 7 of its paintings is fake; they use the new test on all of their paintings. i. What is the predicted number of paintings the test will indicate are fake? ii. What fraction are correctly detected as fake? iii. What is the Bayesian probability that a painting detected as a fake is actually real? Show your working. iv. If two paintings from an art forger (i.e. both fakes) are tested using this test what are the possible numbers of fakes detected and the probability of each number of fakes? v. How many of the fake paintings would have to be tested to ensure at least a 99.99% chance at one or more of the fake paintings is detected? Show your working.
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