245 lines
12 KiB
XML
245 lines
12 KiB
XML
<?xml version="1.0" encoding="UTF-8"?>
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<assessmentItem xmlns="http://www.imsglobal.org/xsd/imsqti_v2p1"
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xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
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xsi:schemaLocation="http://www.imsglobal.org/xsd/imsqti_v2p1 http://www.imsglobal.org/xsd/qti/qtiv2p1/imsqti_v2p1.xsd"
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identifier="adaptive" title="Monty Hall (Take 1)" adaptive="true" timeDependent="false">
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<responseDeclaration identifier="DOOR" cardinality="single" baseType="identifier"/>
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<responseDeclaration identifier="RESPONSE" cardinality="single" baseType="identifier">
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<correctResponse>
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<value>switchStrategy</value>
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</correctResponse>
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</responseDeclaration>
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<outcomeDeclaration identifier="STORY" cardinality="single" baseType="identifier">
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<defaultValue>
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<value>openingGambit</value>
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</defaultValue>
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</outcomeDeclaration>
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<outcomeDeclaration identifier="FEEDBACK" cardinality="single" baseType="identifier"/>
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<outcomeDeclaration identifier="CLOSED" cardinality="multiple" baseType="identifier">
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<defaultValue>
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<value>DoorA</value>
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<value>DoorB</value>
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<value>DoorC</value>
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</defaultValue>
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</outcomeDeclaration>
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<outcomeDeclaration identifier="GOATS" cardinality="multiple" baseType="identifier"/>
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<outcomeDeclaration identifier="PRIZE" cardinality="single" baseType="identifier"/>
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<outcomeDeclaration identifier="FIRSTDOOR" cardinality="single" baseType="identifier"/>
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<outcomeDeclaration identifier="REVEALED" cardinality="single" baseType="identifier"/>
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<outcomeDeclaration identifier="SCORE" cardinality="single" baseType="float"/>
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<itemBody>
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<p>Monty Hall has hidden a prize behind one of these doors.</p>
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<feedbackBlock outcomeIdentifier="STORY" showHide="show" identifier="openingGambit">
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<p>Monty invites you to choose one of the doors but won't let you open it just yet.</p>
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</feedbackBlock>
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<feedbackBlock outcomeIdentifier="STORY" showHide="show" identifier="tempter">
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<p>Monty opens one of the other doors to reveal - a goat!</p>
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<p>He then asks you if you would like to change your mind or to stick with the door you
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originally chose. It's time to make your mind up, which door are you going to
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open?</p>
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</feedbackBlock>
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<feedbackBlock outcomeIdentifier="STORY" showHide="show" identifier="goat">
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<p>Bad luck! When you opened your chosen door it also revealed a goat.</p>
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</feedbackBlock>
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<feedbackBlock outcomeIdentifier="STORY" showHide="show" identifier="prize">
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<p>Congratulations! When you opened your chosen door it revealed a fantastic prize that
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you are now free to take home.</p>
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</feedbackBlock>
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<feedbackBlock outcomeIdentifier="FEEDBACK" showHide="show" identifier="poser">
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<p>Well, whether or not you won the prize did you make your decision by guesswork or
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logical reasoning? The question is, if we allowed you to play this game repeatedly
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what strategy <em>should</em> you adopt?</p>
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</feedbackBlock>
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</itemBody>
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<responseProcessing>
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<setOutcomeValue identifier="completionStatus">
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<baseValue baseType="identifier">incomplete</baseValue>
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</setOutcomeValue>
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<responseCondition>
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<responseIf>
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<!-- Transition from openingGambit to tempter -->
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<and>
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<match>
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<baseValue baseType="identifier">openingGambit</baseValue>
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<variable identifier="STORY"/>
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</match>
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<not>
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<isNull>
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<variable identifier="DOOR"/>
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</isNull>
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</not>
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</and>
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<!-- Remember the first door chosen -->
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<setOutcomeValue identifier="FIRSTDOOR">
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<variable identifier="DOOR"/>
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</setOutcomeValue>
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<!-- Randomly open one of the other two doors -->
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<responseCondition>
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<responseIf>
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<match>
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<variable identifier="DOOR"/>
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<baseValue baseType="identifier">DoorA</baseValue>
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</match>
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<setOutcomeValue identifier="REVEALED">
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<random>
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<multiple>
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<baseValue baseType="identifier">DoorB</baseValue>
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<baseValue baseType="identifier">DoorC</baseValue>
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</multiple>
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</random>
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</setOutcomeValue>
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</responseIf>
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<responseElseIf>
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<match>
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<variable identifier="DOOR"/>
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<baseValue baseType="identifier">DoorB</baseValue>
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</match>
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<setOutcomeValue identifier="REVEALED">
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<random>
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<multiple>
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<baseValue baseType="identifier">DoorA</baseValue>
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<baseValue baseType="identifier">DoorC</baseValue>
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</multiple>
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</random>
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</setOutcomeValue>
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</responseElseIf>
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<responseElse>
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<setOutcomeValue identifier="REVEALED">
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<random>
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<multiple>
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<baseValue baseType="identifier">DoorA</baseValue>
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<baseValue baseType="identifier">DoorB</baseValue>
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</multiple>
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</random>
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</setOutcomeValue>
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</responseElse>
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</responseCondition>
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<setOutcomeValue identifier="CLOSED">
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<delete>
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<variable identifier="REVEALED"/>
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<variable identifier="CLOSED"/>
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</delete>
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</setOutcomeValue>
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<setOutcomeValue identifier="GOATS">
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<multiple>
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<variable identifier="REVEALED"/>
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</multiple>
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</setOutcomeValue>
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<setOutcomeValue identifier="STORY">
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<baseValue baseType="identifier">tempter</baseValue>
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</setOutcomeValue>
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</responseIf>
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<responseElseIf>
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<!-- Transition from tempter to prize or goat -->
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<and>
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<match>
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<baseValue baseType="identifier">tempter</baseValue>
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<variable identifier="STORY"/>
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</match>
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<not>
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<isNull>
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<variable identifier="DOOR"/>
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</isNull>
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</not>
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</and>
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<!-- We score based on whether you switched (and cheat!) -->
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<responseCondition>
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<responseIf>
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<or>
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<match>
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<variable identifier="DOOR"/>
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<variable identifier="FIRSTDOOR"/>
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</match>
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<match>
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<variable identifier="DOOR"/>
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<variable identifier="REVEALED"/>
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</match>
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</or>
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<setOutcomeValue identifier="SCORE">
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<baseValue baseType="float">0</baseValue>
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</setOutcomeValue>
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<setOutcomeValue identifier="GOATS">
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<multiple>
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<variable identifier="GOATS"/>
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<variable identifier="DOOR"/>
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</multiple>
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</setOutcomeValue>
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<setOutcomeValue identifier="STORY">
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<baseValue baseType="identifier">goat</baseValue>
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</setOutcomeValue>
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</responseIf>
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<responseElse>
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<setOutcomeValue identifier="SCORE">
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<baseValue baseType="float">1</baseValue>
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</setOutcomeValue>
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<setOutcomeValue identifier="PRIZE">
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<variable identifier="DOOR"/>
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</setOutcomeValue>
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<setOutcomeValue identifier="STORY">
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<baseValue baseType="identifier">prize</baseValue>
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</setOutcomeValue>
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</responseElse>
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</responseCondition>
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<setOutcomeValue identifier="CLOSED">
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<delete>
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<variable identifier="DOOR"/>
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<variable identifier="CLOSED"/>
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</delete>
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</setOutcomeValue>
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<setOutcomeValue identifier="FEEDBACK">
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<baseValue baseType="identifier">poser</baseValue>
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</setOutcomeValue>
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</responseElseIf>
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<responseElseIf>
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<and>
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<match>
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<variable identifier="FEEDBACK"/>
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<baseValue baseType="identifier">poser</baseValue>
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</match>
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<not>
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<isNull>
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<variable identifier="RESPONSE"/>
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</isNull>
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</not>
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</and>
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<responseCondition>
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<responseIf>
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<match>
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<variable identifier="RESPONSE"/>
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<correct identifier="RESPONSE"/>
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</match>
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<setOutcomeValue identifier="SCORE">
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<sum>
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<variable identifier="SCORE"/>
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<baseValue baseType="float">2</baseValue>
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</sum>
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</setOutcomeValue>
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</responseIf>
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</responseCondition>
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<setOutcomeValue identifier="FEEDBACK">
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<variable identifier="RESPONSE"/>
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</setOutcomeValue>
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<setOutcomeValue identifier="completionStatus">
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<baseValue baseType="identifier">completed</baseValue>
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</setOutcomeValue>
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</responseElseIf>
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</responseCondition>
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</responseProcessing>
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<modalFeedback outcomeIdentifier="FEEDBACK" showHide="show" identifier="stickStrategy">No.
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Initially, the probability of the prize being behind each door is 1/3. Opening a losing door
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can't possibly make this go down for the remaining closed one! In fact you should
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<em>never</em> stick to your original decision.</modalFeedback>
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<modalFeedback outcomeIdentifier="FEEDBACK" showHide="show" identifier="switchStrategy"> Yes,
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you should <em>always</em> switch doors when offered the chance. Congratulations, perhaps
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you should think about a career as a TV game show contestant? </modalFeedback>
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<modalFeedback outcomeIdentifier="FEEDBACK" showHide="show" identifier="noStrategy">
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<p>No, you should infact <em>always</em> switch doors. This problem has fooled many
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mathematicians since it was first posed in an American magazine article and continues to
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present a seemingly paradoxical answer!</p>
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<p>The probability of your first choice door hiding the prize is 1/3 and this can't change.
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But, 2/3 of the time you'll be wrong with your first choice and, by revealing a goat,
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Monty is effectively telling you which door the prize is behind the remaining 2/3 of the
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time! So by switching doors, your chances of getting the prize go up to 2/3!</p>
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</modalFeedback>
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</assessmentItem>
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