<?xml version="1.0" encoding="UTF-8"?>
<assessmentItem xmlns="http://www.imsglobal.org/xsd/imsqti_item_v2p0"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:schemaLocation="http://www.imsglobal.org/xsd/imsqti_item_v2p0 ../imsqti_item_v2p0.xsd"
identifier="adaptiveTemplate" title="Monty Hall (Take 2)" adaptive="true" timeDependent="false">
<responseDeclaration identifier="DOOR" cardinality="single" baseType="identifier"/>
<responseDeclaration identifier="RESPONSE" cardinality="single" baseType="identifier">
<correctResponse>
<value>switchStrategy</value>
</correctResponse>
</responseDeclaration>
<outcomeDeclaration identifier="STORY" cardinality="single" baseType="identifier">
<defaultValue>
<value>openingGambit</value>
</defaultValue>
</outcomeDeclaration>
<outcomeDeclaration identifier="FEEDBACK" cardinality="single" baseType="identifier"/>
<outcomeDeclaration identifier="CLOSED" cardinality="multiple" baseType="identifier">
<defaultValue>
<value>DoorA</value>
<value>DoorB</value>
<value>DoorC</value>
</defaultValue>
</outcomeDeclaration>
<outcomeDeclaration identifier="GOATS" cardinality="multiple" baseType="identifier"/>
<outcomeDeclaration identifier="PRIZE" cardinality="single" baseType="identifier"/>
<outcomeDeclaration identifier="FIRSTDOOR" cardinality="single" baseType="identifier"/>
<outcomeDeclaration identifier="REVEALED" cardinality="single" baseType="identifier"/>
<outcomeDeclaration identifier="SCORE" cardinality="single" baseType="integer"/>
<itemBody>
<p>Monty Hall has hidden a prize behind one of these doors.</p>
<feedbackBlock outcomeIdentifier="STORY" showHide="show" identifier="openingGambit">
<p>Monty invites you to choose one of the doors but won't let you open it just yet.</p>
</feedbackBlock>
<feedbackBlock outcomeIdentifier="STORY" showHide="show" identifier="tempter">
<p>Monty opens one of the other doors to reveal - a goat!</p>
<p>He then asks you if you would like to change your mind or to stick with the door you
originally chose. It's time to make your mind up, which door are you going to open?</p>
</feedbackBlock>
<feedbackBlock outcomeIdentifier="STORY" showHide="show" identifier="goat">
<p>Bad luck! When you opened your chosen door it also revealed a goat.</p>
</feedbackBlock>
<feedbackBlock outcomeIdentifier="STORY" showHide="show" identifier="prize">
<p>Congratulations! When you opened your chosen door it revealed a fantastic prize that
you are now free to take home.</p>
</feedbackBlock>
<choiceInteraction responseIdentifier="DOOR" shuffle="false" maxChoices="1">
<simpleChoice identifier="DoorA">
<feedbackInline outcomeIdentifier="CLOSED" showHide="show" identifier="DoorA">
<img src="redDoor.png" alt="The Red Door"/>
</feedbackInline>
<feedbackInline outcomeIdentifier="GOATS" showHide="show" identifier="DoorA">
<img src="openDoor.png" alt="An open door"/> - this door is now open revealing a goat!</feedbackInline>
<feedbackInline outcomeIdentifier="PRIZE" showHide="show" identifier="DoorA">
<img src="openDoor.png" alt="An open door"/> - this door is now open revealing a
fantastic prize!</feedbackInline>
</simpleChoice>
<simpleChoice identifier="DoorB">
<feedbackInline outcomeIdentifier="CLOSED" showHide="show" identifier="DoorB">
<img src="greenDoor.png" alt="The Green Door"/>
</feedbackInline>
<feedbackInline outcomeIdentifier="GOATS" showHide="show" identifier="DoorB">
<img src="openDoor.png" alt="An open door"/> - this door is now open revealing a goat!</feedbackInline>
<feedbackInline outcomeIdentifier="PRIZE" showHide="show" identifier="DoorB">
<img src="openDoor.png" alt="An open door"/> - this door is now open revealing a
fantastic prize!</feedbackInline>
</simpleChoice>
<simpleChoice identifier="DoorC">
<feedbackInline outcomeIdentifier="CLOSED" showHide="show" identifier="DoorC">
<img src="blueDoor.png" alt="The Blue Door"/>
</feedbackInline>
<feedbackInline outcomeIdentifier="GOATS" showHide="show" identifier="DoorC">
<img src="openDoor.png" alt="An open door"/> - this door is now open revealing a goat!</feedbackInline>
<feedbackInline outcomeIdentifier="PRIZE" showHide="show" identifier="DoorC">
<img src="openDoor.png" alt="An open door"/> - this door is now open revealing a
fantastic prize!</feedbackInline>
</simpleChoice>
</choiceInteraction>
<feedbackBlock outcomeIdentifier="FEEDBACK" showHide="show" identifier="poser">
<p>Well, whether or not you won the prize did you make your decision by guesswork or
logical reasoning? The question is, if we allowed you to play this game repeatedly
what strategy <em>should</em> you adopt?</p>
<choiceInteraction responseIdentifier="RESPONSE" shuffle="true" maxChoices="1">
<simpleChoice identifier="stickStrategy">Always stick to the first door you chose.</simpleChoice>
<simpleChoice identifier="switchStrategy">Always switch to the other closed door
when Monty offers you the chance.</simpleChoice>
<simpleChoice identifier="noStrategy">It really doesn't matter whether you stick or
switch - the outcome's the same.</simpleChoice>
</choiceInteraction>
</feedbackBlock>
</itemBody>
<responseProcessing>
<setOutcomeValue identifier="completion_status">
<baseValue baseType="identifier">incomplete</baseValue>
</setOutcomeValue>
<responseCondition>
<responseIf>
<!-- Transition from openingGambit to tempter -->
<and>
<match>
<baseValue baseType="identifier">openingGambit</baseValue>
<variable identifier="STORY"/>
</match>
<not>
<isNull>
<variable identifier="DOOR"/>
</isNull>
</not>
</and>
<!-- Remember the first door chosen -->
<setOutcomeValue identifier="FIRSTDOOR">
<variable identifier="DOOR"/>
</setOutcomeValue>
<!-- Randomly open one of the other two doors -->
<responseCondition>
<responseIf>
<match>
<variable identifier="DOOR"/>
<baseValue baseType="identifier">DoorA</baseValue>
</match>
<setOutcomeValue identifier="REVEALED">
<random>
<multiple>
<baseValue baseType="identifier">DoorB</baseValue>
<baseValue baseType="identifier">DoorC</baseValue>
</multiple>
</random>
</setOutcomeValue>
</responseIf>
<responseElseIf>
<match>
<variable identifier="DOOR"/>
<baseValue baseType="identifier">DoorB</baseValue>
</match>
<setOutcomeValue identifier="REVEALED">
<random>
<multiple>
<baseValue baseType="identifier">DoorA</baseValue>
<baseValue baseType="identifier">DoorC</baseValue>
</multiple>
</random>
</setOutcomeValue>
</responseElseIf>
<responseElse>
<setOutcomeValue identifier="REVEALED">
<random>
<multiple>
<baseValue baseType="identifier">DoorA</baseValue>
<baseValue baseType="identifier">DoorB</baseValue>
</multiple>
</random>
</setOutcomeValue>
</responseElse>
</responseCondition>
<setOutcomeValue identifier="CLOSED">
<delete>
<variable identifier="REVEALED"/>
<variable identifier="CLOSED"/>
</delete>
</setOutcomeValue>
<setOutcomeValue identifier="GOATS">
<multiple>
<variable identifier="REVEALED"/>
</multiple>
</setOutcomeValue>
<setOutcomeValue identifier="STORY">
<baseValue baseType="identifier">tempter</baseValue>
</setOutcomeValue>
</responseIf>
<responseElseIf>
<!-- Transition from tempter to prize or goat -->
<and>
<match>
<baseValue baseType="identifier">tempter</baseValue>
<variable identifier="STORY"/>
</match>
<not>
<isNull>
<variable identifier="DOOR"/>
</isNull>
</not>
</and>
<!-- We score based on whether you switched (and cheat!) -->
<responseCondition>
<responseIf>
<or>
<match>
<variable identifier="DOOR"/>
<variable identifier="FIRSTDOOR"/>
</match>
<match>
<variable identifier="DOOR"/>
<variable identifier="REVEALED"/>
</match>
</or>
<setOutcomeValue identifier="SCORE">
<baseValue baseType="integer">0</baseValue>
</setOutcomeValue>
<setOutcomeValue identifier="GOATS">
<multiple>
<variable identifier="GOATS"/>
<variable identifier="DOOR"/>
</multiple>
</setOutcomeValue>
<setOutcomeValue identifier="STORY">
<baseValue baseType="identifier">goat</baseValue>
</setOutcomeValue>
</responseIf>
<responseElse>
<setOutcomeValue identifier="SCORE">
<baseValue baseType="integer">1</baseValue>
</setOutcomeValue>
<setOutcomeValue identifier="PRIZE">
<variable identifier="DOOR"/>
</setOutcomeValue>
<setOutcomeValue identifier="STORY">
<baseValue baseType="identifier">prize</baseValue>
</setOutcomeValue>
</responseElse>
</responseCondition>
<setOutcomeValue identifier="CLOSED">
<delete>
<variable identifier="DOOR"/>
<variable identifier="CLOSED"/>
</delete>
</setOutcomeValue>
<setOutcomeValue identifier="FEEDBACK">
<baseValue baseType="identifier">poser</baseValue>
</setOutcomeValue>
</responseElseIf>
<responseElseIf>
<and>
<match>
<variable identifier="FEEDBACK"/>
<baseValue baseType="identifier">poser</baseValue>
</match>
<not>
<isNull>
<variable identifier="RESPONSE"/>
</isNull>
</not>
</and>
<responseCondition>
<responseIf>
<match>
<variable identifier="RESPONSE"/>
<correct identifier="RESPONSE"/>
</match>
<setOutcomeValue identifier="SCORE">
<sum>
<variable identifier="SCORE"/>
<baseValue baseType="integer">2</baseValue>
</sum>
</setOutcomeValue>
</responseIf>
</responseCondition>
<setOutcomeValue identifier="FEEDBACK">
<variable identifier="RESPONSE"/>
</setOutcomeValue>
<setOutcomeValue identifier="completion_status">
<baseValue baseType="identifier">complete</baseValue>
</setOutcomeValue>
</responseElseIf>
</responseCondition>
</responseProcessing>
<modalFeedback outcomeIdentifier="FEEDBACK" showHide="show" identifier="stickStrategy">No.
Initially, the probability of the prize being behind each door is 1/3. Opening a losing door
can't possibly make this go down for the remaining closed one! In fact you should
<em>never</em> stick to your original decision.</modalFeedback>
<modalFeedback outcomeIdentifier="FEEDBACK" showHide="show" identifier="switchStrategy"> Yes,
you should <em>always</em> switch doors when offered the chance. Congratulations, perhaps
you should think about a career as a TV game show contestant? </modalFeedback>
<modalFeedback outcomeIdentifier="FEEDBACK" showHide="show" identifier="noStrategy">
<p>No, you should infact <em>always</em> switch doors. This problem has fooled many
mathematicians since it was first posed in an American magazine article and continues to
present a seemingly paradoxical answer!</p>
<p>The probability of your first choice door hiding the prize is 1/3 and this can't change.
But, 2/3 of the time you'll be wrong with your first choice and, by revealing a goat,
Monty is effectively telling you which door the prize is behind the remaining 2/3 of the
time! So by switching doors, your chances of getting the prize go up to 2/3!</p>
</modalFeedback>
</assessmentItem>