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(upbeat synth music)
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- [Instructor] In the previous movie, I described a problem
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where you will determine the probability,
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an item is genuine when it's reported genuine.
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And an item is counterfeit when reported
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counterfeit by museum appraisers and curators
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based on the base rate of genuine items,
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comprising 70% of the collection
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and an appraiser accuracy rate of 90%.
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So let's go ahead and fill in the worksheet
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and perform our calculations.
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I'll click in cell B6.
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The probability in item is genuine is given in B3.
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So in B6 I'll, type equal and B3.
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That means that the probability it is counterfeit
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or fake, not real is 1 minus 70%,
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so in B7 we'll type equal
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one minus and our base rates in B3, so enter.
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70 and 30 is 100, which is correct.
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Now we need to determine the probability
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the appraisers are correct or incorrect.
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So in B9, I'll type equal.
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The probability they're correct is their accuracy,
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so that's in B4.
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And as with the probability of an item being counterfeit
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the probability of them being incorrect
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is 1 minus the probability they are correct.
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So in B10
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equal 1 minus
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B4 and enter,
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and we get 10%.
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90 plus 10 equals 100,
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so we're good there.
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Now we can go over to our classification matrix
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and calculate the probability of each one of our scenarios.
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So we have an item actually being genuine
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and being reported genuine.
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So in E4 I'll type equal
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and the base rate of them being genuine is 70%.
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And I have that probability in B6.
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And then I want to multiply that
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by the probability that the curator is correct,
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that's in B9 and enter.
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So that's the probability for that scenario.
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Now, in E5, I need to give the probability
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that an item is reported as genuine
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but is actually counterfeit,
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so in other words, a mistake was made, so equal.
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And I will have an item
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is being counterfeit.
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that is in B7.
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And we'll multiply that by the probability,
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that the appraiser is incorrect,
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and that is in cell B10 and enter,
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so we have 3%.
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Now we have reported counterfeit and actually genuine,
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so again, a mistake was made.
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So we in F4 we'll type in equal sign
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and we're multiplying the probability
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that the item is actually genuine,
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that is in B6.
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By the probability that the appraiser made
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a mistake that's in B10, enter.
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So that's 7%.
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And then in F5, we need to calculate the probability
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that an appraiser correctly identified a counterfeit object.
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So in F5 equal, and we are multiplying the probability
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that the item is counterfeit that's in B7.
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By the probability that the appraiser is correct,
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that's in B9, enter.
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And we get 27%.
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And we can look at our values
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to make sure that everything lines up.
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So our correct guesses are 63% and 27%
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of the time that's 90, that is our probability, correct.
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And 7+3 is 10,
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and that is the probability
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of the appraiser being incorrect.
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Now we can calculate the probability
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that an item is genuine when reported genuine
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and counterfeit reported counterfeit.
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So I'll click in cell E8 type an equal sign.
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And we need to calculate the percentage
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of times that an item is reported as genuine
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and it actually is.
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So reported genuine is and cell E4
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divide it by the total number of times
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an item is identified as genuine,
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both right and wrong.
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And that is adding E4 and E5.
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So I'll type the left parenthesis E4+E5,
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right parenthesis and tab,
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and we get 95%.
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Now we can calculate the probability
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an item is actually counterfeit
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when it's reported counterfeit.
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So in F8 I'll type equal
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and we need to divide
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the correct guesses by total guesses.
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For this column, the correct guesses are in F5,
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then I'll type a forward slash for division,
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left parentheses and we need to add the total number
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of times that an item is reported as counterfeit,
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both right and wrong.
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So that's F4+ F5, right parentheses and enter,
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and we get 79%.
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And so it appears that our team will do a very good job
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of identifying genuine items with very little error
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and still a pretty good
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but not quite as good job identifying counterfeits.
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I hope you enjoyed this problem.
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Bayesian analysis is very different
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from other types analysis that we typically do in Excel,
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so don't worry if you didn't get it right on the first time.
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Take a few minutes, walk away from the workbook,
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come back and feel free to try again.
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