Expectation Value Simulator: Spinner Probability Experiment
2015-09-13 08:07
This GeoGebra applet demonstrates the concept of expected value in probability and statistics. Using a customizable circular spinner composed of sectors and angles, users can simulate random experiments: buttons trigger single or ten spins, while the system automatically tracks outcome frequencies and corresponding payoffs (money1/money2), computing a running average (avg) in real time. As the num
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.529.0" app="classic" platform="w" id="80b42e48-4aba-4ac4-9760-111e982a8341" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1000" height="690" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.471" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1,1,1" size="400" window="116,66,1048,686" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="91" window="276,169,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="1,1" size="211" window="100,100,250,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 22 , 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1" size="765" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="3" size="471" window="100,100,600,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="1" size="519" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="7" help="false" />
<input show="false" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="20"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="471" height="688"/>
<coordSystem xZero="239.69655340270458" yZero="208.9982459051304" scale="188.5454772781909" yscale="188.54547727819087"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="0.1" distY="0.1" distTheta="0.2617993877991494"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="519" height="688"/>
<coordSystem xZero="219.0000000000001" yZero="319.0000000000001" scale="49.999999999999986" yscale="50.00000000000003"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="0.5" distY="0.5" distTheta="0.5235987755982988"/>
</euclidianView>
<algebraView>
<mode val="1"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="1"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="numeric" label="index">
<value val="277"/>
<show object="false" label="true"/>
<objColor r="255" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="2"/>
<labelMode val="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="i°" a1="i" a2="0.5" a3="359.5" a4="1"/>
<output a0="listTheta"/>
</command>
<element type="list" label="listTheta">
<show object="true" label="true"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<element type="button" label="buttonOne">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="19" y="19"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<javascript val="spin(1);"/>
<font serif="false" sizeM="2.5" size="30" style="0"/>
<caption val="Spin once"/>
</element>
<expression label="theta" exp="listTheta(index)" />
<element type="angle" label="theta">
<angleStyle val="0"/>
<value val="4.825835381764321"/>
<show object="false" label="true" ev="3"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="2"/>
<arcSize val="30"/>
<selectionAllowed val="false"/>
</element>
<expression label="P" exp="(1; theta)" type="point" />
<element type="point" label="P">
<show object="false" label="true"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.11320321376790658" y="-0.9935718556765876" z="1"/>
<coordStyle style="polar"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Circle">
<input a0="(0, 0)" a1="1"/>
<output a0="c"/>
</command>
<element type="conic" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-1" A3="0" A4="0" A5="0"/>
<eqnStyle style="specific"/>
</element>
<element type="point" label="A">
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="5" y="13"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<coords x="1" y="0" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="point" label="O">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="-13" y="32"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<coords x="0" y="0" z="1"/>
<pointSize val="6"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="O" a1="P"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="true" label="false"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0.11320321376790658" y="-0.9935718556765876" z="0"/>
<lineStyle thickness="11" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint exp="O"/>
</element>
<command name="Point">
<input a0="Sequence[(1; i°), i, 5, 355, 5]"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="false" label="false" ev="4"/>
<condition showObject="adjust ≠ 0"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="3" y="-13"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="6.123233995736766e-17" y="1" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Angle">
<input a0="A" a1="O" a2="B"/>
<output a0="alpha"/>
</command>
<element type="angle" label="alpha">
<angleStyle val="0"/>
<value val="1.5707963267948966"/>
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="24" y="-3"/>
<labelMode val="2"/>
<lineStyle thickness="3" type="0" typeHidden="2"/>
<arcSize val="30"/>
<selectionAllowed val="false"/>
</element>
<command name="CircleSector">
<input a0="O" a1="A" a2="B"/>
<output a0="s"/>
</command>
<element type="conicpart" label="s">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.4000000059604645"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="1" type="0" typeHidden="1"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="-1" A3="0" A4="0" A5="0"/>
<eqnStyle style="implicit"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="count1">
<value val="0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="2"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="count2">
<value val="0"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="2"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="button" label="buttonReset">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelOffset x="19" y="94"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[count1,0]
SetValue[count2,0]"/>
<font serif="false" sizeM="2" size="20" style="0"/>
<caption val="Reset"/>
</element>
<element type="boolean" label="adjust">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelOffset x="8" y="430"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Adjust angle"/>
</element>
<expression label="M1" exp="(0.5; alpha / 2)" type="point" />
<element type="point" label="M1">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="0.3535533905932738" y="0.35355339059327373" z="1"/>
<coordStyle style="polar"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="M2" exp="(0.5; (alpha + 360°) / 2)" type="point" />
<element type="point" label="M2">
<show object="false" label="true"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="-0.35355339059327384" y="-0.35355339059327373" z="1"/>
<coordStyle style="polar"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="money1">
<value val="60"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="2"/>
<labelMode val="1"/>
<slider min="0" max="1000" absoluteScreenLocation="true" width="200" fixed="true" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="money2">
<value val="20"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="2"/>
<labelMode val="1"/>
<slider min="0" max="1000" absoluteScreenLocation="true" width="200" fixed="true" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="text1" exp=""$" + money1" />
<element type="text" label="text1">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="true" sizeM="4" size="60" style="0"/>
<startPoint exp="M1"/>
<labelOffset x="-41" y="21"/>
</element>
<expression label="text2" exp=""$" + money2" />
<element type="text" label="text2">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<font serif="true" sizeM="4" size="60" style="0"/>
<startPoint exp="M2"/>
<labelOffset x="-72" y="34"/>
</element>
<expression label="avg" exp="((money1 * count1) + (money2 * count2)) / (count1 + count2)" />
<element type="numeric" label="avg">
<value val="NaN"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<selectionAllowed val="false"/>
</element>
<expression label="ev" exp="(money1 * alpha / (360°)) + (money2 * (360° - alpha) / (360°))" />
<element type="numeric" label="ev">
<value val="30"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<selectionAllowed val="false"/>
</element>
<element type="boolean" label="showEV">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="8" y="506"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Expected amount in each turn"/>
</element>
<element type="button" label="buttonTen">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="194" y="18"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<javascript val="spin(10);"/>
<font serif="false" sizeM="2.5" size="30" style="0"/>
<caption val="Spin 10 times"/>
</element>
<expression label="text5" exp=""=\$" + (LaTeX[money1]) + "×\red{\frac{" + (LaTeX[alpha / °]) + "}{360}}+\$" + (LaTeX[money2]) + "×\red{\frac{" + (LaTeX[360 - alpha / °]) + "}{360}}\\
=\underline{\underline{\$\;" + (LaTeX[ev]) + "}}"" />
<element type="text" label="text5">
<show object="true" label="false" ev="8"/>
<condition showObject="showEV ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<absoluteScreenLocation x="36" y="541"/>
</element>
<command name="Textfield">
<input a0="money1"/>
<output a0="InputBox1"/>
</command>
<element type="textfield" label="InputBox1">
<show object="true" label="false"/>
<condition showObject="adjust2 ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<bgColor r="125" g="125" b="255" alpha="255"/>
<layer val="2"/>
<labelOffset x="237" y="473"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<ggbscript onUpdate="RunClickScript[buttonReset]"/>
<linkedGeo exp="money1"/>
<length val="3"/>
<caption val="-"/>
</element>
<command name="Textfield">
<input a0="money2"/>
<output a0="InputBox2"/>
</command>
<element type="textfield" label="InputBox2">
<show object="true" label="false"/>
<condition showObject="adjust2 ≠ 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="224" g="224" b="224" alpha="255"/>
<layer val="2"/>
<labelOffset x="296" y="473"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<ggbscript onUpdate="RunClickScript[buttonReset]"/>
<linkedGeo exp="money2"/>
<length val="3"/>
<caption val="-"/>
</element>
<element type="boolean" label="adjust2">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="197" y="430"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Adjust amount"/>
</element>
<expression label="textAvg" exp=""=\frac{\$" + (LaTeX[money1]) + " ×\red{ " + (LaTeX[count1]) + "}+\$" + (LaTeX[money2]) + " ×\red{ " + (LaTeX[count2]) + "}}{\red{" + (LaTeX[count1 + count2]) + " }}"" />
<element type="text" label="textAvg">
<show object="false" label="true" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<startPoint x="-3.9200000000000035" y="-0.6599999999999975" z="1"/>
</element>
<element type="button" label="button0">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelOffset x="444" y="28"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[lang,If[lang==1,2,1]]
RunClickScript[buttonLang]

"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="中文"/>
</element>
<element type="button" label="buttonLang">
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelOffset x="439" y="22"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetCaption[button0,If[lang==1,"ENG","中文"]]
SetCaption[buttonOne,If[lang==1,"轉動1次","Spin once"]]
SetCaption[buttonTen,If[lang==1,"轉動10次","Spin 10 times"]]
SetCaption[buttonReset,If[lang==1,"重設","Reset"]]
SetCaption[adjust,If[lang==1,"調整角度","Adjust angle"]]
SetCaption[adjust2,If[lang==1,"調整金額","Adjust amount"]]
SetCaption[showEV,If[lang==1,"每次獎金的期望值","Expected amount in each turn"]]"/>
<font serif="false" sizeM="2" size="20" style="0"/>
</element>
<element type="numeric" label="lang">
<value val="2"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="2"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="text4" exp=""\text{" + (LaTeX[If[lang ≟ 1, "平均每次獎金", "Average amount got in each turn"]]) + "}\\\vspace{60}" + (LaTeX[If[count1 > 0 ∧ count2 > 0, textAvg, ""]]) + "\\\vspace{40}
=\underline{\underline{\$\;" + (LaTeX[avg]) + "}}"" />
<element type="text" label="text4">
<show object="false" label="false" ev="11"/>
<condition showObject="count1 + count2 > 0"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<startPoint x="-3.9448029189007556" y="-0.7551970810992362" z="1"/>
</element>
<expression label="text3" exp=""\text{" + (LaTeX[If[lang ≟ 1, "總次數", "No. of turns"]]) + "} =\red{ " + (LaTeX[count1 + count2]) + "}\\
\text{" + (LaTeX[If[lang ≟ 1, "中 ", "No. of turns hitting "]]) + "}\$" + (LaTeX[money1]) + "\text{" + (LaTeX[If[lang ≟ 1, " 次數", ""]]) + "} =\red{ " + (LaTeX[count1]) + "}\\
\text{" + (LaTeX[If[lang ≟ 1, "中 ", "No. of turns hitting "]]) + "}\$" + (LaTeX[money2]) + "\text{" + (LaTeX[If[lang ≟ 1, " 次數", ""]]) + "} =\red{ " + (LaTeX[count2]) + "}"" />
<element type="text" label="text3">
<show object="true" label="false" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<startPoint x="-3.944802918900751" y="2.9421751709109447" z="1"/>
</element>
</construction>
</geogebra>