#####    Quiz 3 Prep Code block: 499 lines of code
# DESCRIPTION  11
# Probability
# WeBWorK problem written by Tim Payer, <tsp1@humboldt.edu>
# ENDDESCRIPTION

## DBsubject(Probability)
## DBchapter(Random Variables)
## DBsection(Expectation)
## Institution(Humboldt State University)
## Author(Tim Payer)
## KEYWORDS(probability, addition, notation)

DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGML.pl",
"parserFormulaUpToConstant.pl",
"niceTables.pl",
"PGunion.pl",
"parserPopUp.pl",
"weightedGrader.pl"
);

TEXT(beginproblem());
install_weighted_grader();

Context("Numeric");
Context()->flags->set(
  tolerance => 0.0001,
  tolType => "absolute",
);


# To switch off the algorithmic data un-comment the following 3 lines:
# and then Comment (#) the 3 random assignments of toes and tails.
# $a = 12;
# $o = 21;
# $b = 4;

$a = random(6, 17,1);  # Extra Toes percentage
$o = random(19, 31,1); # Kinked tail percentage
$b = random(1, $a-2,1); # both percentage
$ap = $a/100;
$op = $o/100;
$bp = $b/100;
$na = 1-$ap; # No Extra toes
$no = 1-$op; # No kinked tails
$nb = 1-$bp;# Not both

$popup11 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "b");

$popup01 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "13");

$popup12 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "v");
$ans1 = Compute("1-$o/100+$b/100");

$popup21 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "j");

$popup02 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "6");

$popup22 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "s");
$ans2 = Compute("$a/100-$b/100");

$popup31 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "i");

$popup03 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "9");

$popup32 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "x");
$ans3 = Compute("1-$o/100");

$popup41 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "e");

$popup04 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "2");

$popup42 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "t");
$ans4 = Compute("$b/100");

$popup51 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "d");

$popup05 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "5");

$popup52 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "o");
$ans5 = Compute("($a+$o-$b)/100");

$popup61 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "h");

$popup06 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "8");

$popup62 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "m");
$ans6 = Compute("1-$b/100");

$popup71 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "c");

$popup07 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "12");

$popup72 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "n");
$ans7 = Compute("1+($b-$a)/100");

$popup81 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "l");

$popup08 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "11");

$popup82 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "p");
$ans8 = Compute("1-($o+$a)/100+2*$b/100");

$popup91 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "g");

$popup09 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "4");

$popup92 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "u");
$ans9 = Compute(" ($o-$b)/100");

$popup101 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "k");

$popup010 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "10");

$popup102 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "r");
$ans10 = Compute("1+ ($b-$a-$o)/100");

$popup111 = PopUp(
["Choose:", "a", "b", "c", "d", "e","f","g", "h", "i","j", "k", "l" ], "a");

$popup011 = PopUp(
["Choose:", "1", "2", "3", "4", "5","6","7", "8", "9","10", "11", "12", "13", "14", "15","16" ], "14");

$popup112 = PopUp(
["Choose:", "m", "n","o", "p", "q", "r","s", "t", "u", "v","w", "x" ], "w");
$ans11 = Compute("1+ -$a/100");


#Unicode errors due to non acceptance of: "P(B ~~x{2229} F)"
# Apparently the unicode wont work here?  "~~x{2229}" wont render
# I will replace the "n" with intersection symbols once the proper code is found.
# And I still need to weight the responses with points.


BEGIN_PGML
*Drawn From Lecture Notes: Week 3 Day 3.*
[@
DataTable(
  [
    [["$BBOLD Q3 Prep 1) $EBOLD  A population of cats on a ranch are either polydactyl (having extra toes) or have a kinked tail or some combination of both or neither.  $a% of the cats are poldactyl,  $o% have kinked tails while  $b% have both attributes. Determine the probability of drawing a cat from the ranch population for each of the given scenarios below. Use the declared event variables of T and K below to select the correct probability notation from the table that will best describe each scenario. Each description must be translated first into concise probability notation, then find its associated shaded Venn diagram and then select the expanded notation. It is the expanded form that will enable you to calculate each probability with accuracy to the fourth decimal. $BR $BR $BBOLD Note:$EBOLD On the hard copy Quiz 3 in lab you must create your own event variables. When declaring variables use a single letter for a single event. Describe the event with a sentence. DO NOT couple events in your declaration. See the table below for a comparison of correct and incorrect variable declarations."],"A Cat's Polydactyl Paw: $BR".image("polydactyl_1.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of a cat extending his poldactyl paw while reclining on a couch."')."$BR A Cat's Kinked Tail: $BR".image("kink_tail_1.png", width=>500, height=>374, tex_size=>700, extra_html_tags=>'alt="A photo of a cats furry kinked tail."')."$BR photos by Wikimedia Commons"],
  ], 
  caption => "A Population of Cats with Two Possible Attributes: Extra Toes and Kinked tails.",
  midrules => 0,
align => "p{4in} p{2.2in}",
);
@]***  
  
  
[@
DataTable(
  [
    [["Properly Declared Event Variables:", headerrow => 1],"These are NOT correct declarations:"],
    [["T = A cat with extra toes is drawn."],"\\(\\quad\\)T = toes, \\(\\quad\\) T = $a%,  \\(\\quad\\)   B = both"],
    [["K = A cat with a kinked tail is drawn."],"\\(\\quad\\)K = kinks, \\(\\quad\\)    K = $o%,  \\(\\quad\\)   KT = both \\(\\quad\\)"]
  ], 
  caption => 'Declaration of Event Variables:',
  midrules => 1,
align => '|p{3in}| p{3in}|',
);
@]***
  
  
    Use the table below to choose the letter next to the correct probability notation for each question. The first column holds translations from English to probability notation. The second column hold expanded probability notation.  
  
  
[@
DataTable(
  [
    [["Translated Notations:", headerrow => 1],"Expanded Notations:"],
    [["a.) \\(\\quad  P\\left(\\overline T\\right) \\)"],"m.) \\(\\quad 1 - P(T \\cap K)\\)"],
    [["b.) \\(\\quad  P\\left(T \\cup \\overline K\\right) \\)"],"n.) \\(\\quad P\\left(\\overline T\\right) + P(T \\cap K)\\)"],
    [["c.) \\( \\quad P\\left(\\overline T \\cup K \\right)  \\) "],"o.) \\(\\quad P(T) + P(K) - P(T \\cap K) \\) "],
    [["d.) \\(\\quad P(T \\cup K)  \\)"],"p.) \\( \\quad P\\left(\\overline T \\right) - P(K) + 2 \\cdot P(T \\cap K) \\)"],
    [["e.) \\(\\quad P(T \\cap K)  \\)"],"q.) \\(\\quad1 - P(T) - P(K) + P(T \\cup K)  \\)"],
    [["f.) \\(\\quad P \\left((T \\cap K) \\cap \\left(\\overline T \\cap \\overline K \\right) \\right) \\)  "],"r.) \\(\\quad 1 - P(T) - P(K) + P(T \\cap K) \\) "],
    [["g.) \\(\\quad  P\\left(\\overline T \\cap K \\right)   \\)  "],"s.) \\(\\quad P(T) - P(T \\cap K) \\) "],
    [["h.) \\(\\quad P\\left(\\overline T \\cup \\overline K \\right)  \\) "],"t.) \\(\\quad P(T \\cap K) \\) "],
    [["i.) \\(\\quad  P \\left(\\overline K \\right) \\) "],"u.) \\(\\quad P(K) - P(T \\cap K) \\) "],
    [["j.) \\(\\quad  P \\left(T \\cap \\overline K \\right)\\) "],"v.) \\(\\quad P \\left(\\overline K \\right) + P(T \\cap K) \\)"],
    [["k.) \\(\\quad  P \\left(\\overline T \\cap \\overline K \\right) \\)   "],"w.) \\(\\quad 1 - P(T) \\) "],
    [["l.) \\(\\quad P \\left((T \\cap K) \\cup \\left(\\overline T \\cap \\overline K \\right) \\right) \\)   "],"x.) \\(\\quad1 - P(K)  \\) "]
  ], 
  caption => "Probability Notations:",
  midrules => 1,
align => "|p{2.5in}| p{2.8in}|",
);
@]***  
  
  
[@
DataTable(
  [
    [["Choose the correct probability translation from the lettered notations of a-l in the table above:"],"Choose the event scenario diagram from the 16 selections offered at the bottom of this page.","Choose the correct expanded notation selections of m-x in the table above:","Calculate the probability with fourth decimal accuracy:"],
  ], 
  caption => "Choose the correct probability notations and event diagram scenarios for each event. Then calculate the probability.",
  midrules => 1,
align => '| p{3in}|p{2.6in}| p{2.8in}|p{1.2in}|',
);
@]***



*Q3p.1)*  Find the probability of drawing a cat that has extra toes or does not have a kinked tail.

[$popup11->menu]* = [$popup01->menu]* =[$popup12->menu]* = [______]

*Q3p.2)*  Find the probability of drawing a cat that has extra toes but not a kinked tail.  

[$popup21->menu]* = [$popup02->menu]* =[$popup22->menu]* = [______]


*Q3p.3)*  Find the probability of drawing a cat that does not have a kinked tail.    

[$popup31->menu]* = [$popup03->menu]* =[$popup32->menu]* = [______]


*Q3p.4)*  Find the probability of drawing a cat that has extra toes and a kinked tail.

[$popup41->menu]* = [$popup04->menu]* = [$popup42->menu]* = [______]


*Q3p.5)*  Find the probability of drawing a cat that either has extra toes or a kinked tail.

[$popup51->menu]* = [$popup05->menu]* = [$popup52->menu]* = [______]


*Q3p.6)*  Find the probability of drawing a cat that either does not have extra toes or does not have a kinked tail.

[$popup61->menu]* = [$popup06->menu]* = [$popup62->menu]* = [______]


*Q3p.7)*  Find the probability of drawing a cat that does not have extra toes or has a kinked tail.

[$popup71->menu]* = [$popup07->menu]* =[$popup72->menu]* = [______]


*Q3p.8)*  Find the probability of drawing a cat that either has extra toes with a kinked tail or has neither.  

[$popup81->menu]* = [$popup08->menu]* =[$popup82->menu]* = [______]


*Q3p.9)*  Find the probability of drawing a cat without extra toes but with a kinked tail.

[$popup91->menu]* = [$popup09->menu]* = [$popup92->menu]* = [______]


*Q3p.10)*  Find the probability of drawing a cat that does not have extra toes nor a kinked tail.

[$popup101->menu]* = [$popup010->menu]* =[$popup102->menu]* = [______]


*Q3p.11)*  Find the probability of drawing a cat that does not have extra toes.

[$popup111->menu]* = [$popup011->menu]* = [$popup112->menu]* = [______]

  
  
[@
DataTable(
  [
    [[image( "Scenario_1.png", width=>450, height=>439,  
tex_size=>700, extra_html_tags=>'alt="Scenario_1 " ' ) ],image( "Scenario_2.png", width=>458, height=>476,  
tex_size=>700, extra_html_tags=>'alt="Scenario_2 " ' ),image( "Scenario_3.png", width=>447, height=>484,  
tex_size=>700, extra_html_tags=>'alt="Scenario_3 " ' ),image( "Scenario_4.png", width=>441, height=>479,  
tex_size=>700, extra_html_tags=>'alt="Scenario_4 " ' )],
    [[image( "Scenario_5.png", width=>438, height=>477,  
tex_size=>700, extra_html_tags=>'alt="Scenario_5 " ' )],image( "Scenario_6.png", width=>443, height=>470,  
tex_size=>700, extra_html_tags=>'alt="Scenario_6 " ' ),image( "Scenario_7.png", width=>451, height=>484,  
tex_size=>700, extra_html_tags=>'alt="Scenario_7 " ' ),image( "Scenario_8.png", width=>443, height=>485,  
tex_size=>700, extra_html_tags=>'alt="Scenario_8 " ' )], 
    [[image( "Scenario_9.png", width=>462, height=>480,  
tex_size=>700, extra_html_tags=>'alt="Scenario_9 " ' )],image( "Scenario_10.png", width=>436, height=>480,  
tex_size=>700, extra_html_tags=>'alt="Scenario_10 " ' ),image( "Scenario_11.png", width=>455, height=>480,  
tex_size=>700, extra_html_tags=>'alt="Scenario_11 " ' ),image( "Scenario_12.png", width=>461, height=>497,  
tex_size=>700, extra_html_tags=>'alt="Scenario_12" ' )],
    [[image( "Scenario_13.png", width=>446, height=>489,  
tex_size=>700, extra_html_tags=>'alt="Scenario_13 " ' )],image( "Scenario_14.png", width=>451, height=>495,  
tex_size=>700, extra_html_tags=>'alt="Scenario_14 " ' ),image( "Scenario_15.png", width=>455, height=>483,  
tex_size=>700, extra_html_tags=>'alt="Scenario_15 " ' ),image( "Scenario_16.png", width=>446, height=>472,  
tex_size=>700, extra_html_tags=>'alt="Scenario_16 " ' )]
  ], 
  caption => "Event Diagram Scenarios: 1 - 16",
  midrules => 1,
align => "|p{1.8in}| p{1.8in}|p{1.8in}|p{1.8in}|",
);
@]***
END_PGML


BEGIN_PGML_SOLUTION
*SOLUTION*  
  
  
  [@
DataTable(
  [
    [["$BBOLD Q3p.1) $EBOLD \\(\\quad  P \\left(T \\cup \\overline K \\right) = P\\left(\\overline K\\right) + P(T \\cap K) \\) $BR $BR \\( \\quad \\quad \\quad \\quad P \\left(T \\cup \\overline K \\right) = $no + $bp = $ans1 \\)"],image("Scenario_13.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 13 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.1)  Find the probability of drawing a cat that has extra toes or does not have a kinked tail.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  
  
  [@
DataTable(
  [
    [["$BBOLD Q3p.2) $EBOLD \\(\\quad  P \\left(T \\cap \\overline K \\right) = P\\left(T\\right)-P(T \\cap K) \\) $BR $BR \\( \\quad \\quad \\quad \\quad  P \\left(T \\cap \\overline K \\right) = $ap - $bp = $ans2 \\)"],image("Scenario_6.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 6 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.2)  Find the probability of drawing a cat that has extra toes but not a kinked tail.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  
  
  [@
DataTable(
  [
    [["$BBOLD Q3p.3) $EBOLD \\(\\quad  P \\left(\\overline K \\right) = 1 - P(K) \\) $BR $BR \\( \\quad \\quad \\quad \\quad  P \\left(\\overline K \\right) = 1 - $op = $ans3 \\)"],image("Scenario_9.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 9 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.3)  Find the probability of drawing a cat that does not have a kinked tail.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  
  
 [@
DataTable(
  [
    [["$BBOLD Q3p.4) $EBOLD \\(\\quad  P \\left(T \\cap K \\right) = P \\left(T \\cap K \\right) = $ans4 \\)"],image("Scenario_2.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 2 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.4)  Find the probability of drawing a cat that has extra toes and a kinked tail.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  
  
  [@
DataTable(
  [
    [["$BBOLD Q3p.5) $EBOLD \\(\\quad  P \\left(T \\cup K \\right) = P\\left(T\\right) + P(K) - P\\left( T \\cap K\\right) \\) $BR $BR\\( \\quad \\quad \\quad \\quad P \\left(T \\cup K \\right) = $ap +$op - $bp = $ans5 \\)"],image("Scenario_5.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 5 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.5)  Find the probability of drawing a cat that either has extra toes or a kinked tail.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  
  
[@
DataTable(
  [
    [["$BBOLD Q3p.6) $EBOLD \\(\\quad  P \\left(\\overline T \\cup \\overline K \\right) = 1 - P\\left(T \\cap K\\right)\\) $BR $BR\\( \\quad \\quad \\quad \\quad P\\left(\\overline T \\cup \\overline K \\right)  = 1 - $bp = $ans6 \\)"],image("Scenario_8.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 8 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.6)  Find the probability of drawing a cat that either does not have extra toes or does not have a kinked tail.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  
  
[@
DataTable(
  [
    [["$BBOLD Q3p.7) $EBOLD \\(\\quad  P \\left(\\overline T \\cup K \\right) =  P\\left( \\overline T \\right) + P\\left(T \\cap K\\right) \\) $BR $BR\\( \\quad \\quad \\quad \\quad P\\left(\\overline T \\cup K \\right)  = 1 -$ap + $bp = $ans7 \\)"],image("Scenario_12.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 12 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.7)  Find the probability of drawing a cat that does not have extra toes or has a kinked tail.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  
  
[@
DataTable(
  [
    [["$BBOLD Q3p.8) $EBOLD \\(\\quad  P \\left(\\left( T \\cap  K \\right)\\cup \\left(\\overline T \\cap \\overline K \\right)\\right) = 1-  P\\left(T \\right) -  P\\left(K \\right) + 2\\cdot P\\left(T \\cap K\\right) \\) $BR $BR \\( \\quad \\quad \\quad  P \\left(\\left( T \\cap  K \\right)\\cup \\left(\\overline T \\cap \\overline K \\right)\\right)= 1 -$ap - $op + 2 \\cdot $bp = $ans8 \\)"],image("Scenario_11.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 11 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.8)  Find the probability of drawing a cat that either has extra toes with a kinked tail or has neither.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  
  
[@
DataTable(
  [
    [["$BBOLD Q3p.9) $EBOLD \\(\\quad  P \\left(\\overline T \\cap K \\right) =  P\\left( K \\right) - P\\left(T \\cap K\\right) \\) $BR $BR\\( \\quad \\quad \\quad \\quad P\\left(\\overline T \\cap K \\right) = $op - $bp = $ans9 \\)"],image("Scenario_4.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 4 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.9)  Find the probability of drawing a cat without extra toes but with a kinked tail.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  
  
  [@
DataTable(
  [
    [["$BBOLD Q3p.10) $EBOLD \\(\\quad  P \\left(\\overline T \\cap \\overline K \\right) = 1-  P\\left( T \\right) -  P\\left( K \\right) + P\\left(T \\cap K\\right) \\) $BR $BR \\( \\quad \\quad \\quad \\quad P \\left(\\overline T \\cap \\overline K \\right) = 1- $ap - $op + $bp = $ans10 \\)"],image("Scenario_10.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 10 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.10)  Find the probability of drawing a cat that does not have extra toes nor a kinked tail.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  
  
  [@
DataTable(
  [
    [["$BBOLD Q3p.11) $EBOLD \\(\\quad  P \\left(\\overline T \\right) = 1 - P\\left( T \\right) \\) $BR $BR\\( \\quad \\quad \\quad \\quad P\\left(\\overline T \\right) = 1 - $ap = $ans11 \\)"],image("Scenario_14.png", width=>499, height=>497, tex_size=>700, extra_html_tags=>'alt="A photo of Scenario 14 showing the shading of the probability space."')],
  ], 
  caption => "Q3p.11)  Find the probability of drawing a cat that does not have extra toes.",
  midrules => 0,
align => "p{6in} p{1.8in}",
);
@]***  


END_PGML_SOLUTION

WEIGHTED_ANS( ($popup11)->cmp, 1 );
WEIGHTED_ANS( ($popup01)->cmp, 2 );
WEIGHTED_ANS( ($popup12)->cmp, 2 );
WEIGHTED_ANS( ($ans1)->cmp, 4 );
WEIGHTED_ANS( ($popup21)->cmp, 1 );
WEIGHTED_ANS( ($popup02)->cmp, 2 );
WEIGHTED_ANS( ($popup22)->cmp, 2 );
WEIGHTED_ANS( ($ans2)->cmp, 4 );
WEIGHTED_ANS( ($popup31)->cmp, 1 );
WEIGHTED_ANS( ($popup03)->cmp, 2 );
WEIGHTED_ANS( ($popup32)->cmp, 2 );
WEIGHTED_ANS( ($ans3)->cmp, 5 );
WEIGHTED_ANS( ($popup41)->cmp, 1 );
WEIGHTED_ANS( ($popup04)->cmp, 2 );
WEIGHTED_ANS( ($popup42)->cmp, 2 );
WEIGHTED_ANS( ($ans4)->cmp, 4 );
WEIGHTED_ANS( ($popup51)->cmp, 1 );
WEIGHTED_ANS( ($popup05)->cmp, 2 );
WEIGHTED_ANS( ($popup52)->cmp, 2 );
WEIGHTED_ANS( ($ans5)->cmp, 4 );
WEIGHTED_ANS( ($popup61)->cmp, 1 );
WEIGHTED_ANS( ($popup06)->cmp, 2 );
WEIGHTED_ANS( ($popup62)->cmp, 2 );
WEIGHTED_ANS( ($ans6)->cmp, 4 );
WEIGHTED_ANS( ($popup71)->cmp, 1 );
WEIGHTED_ANS( ($popup07)->cmp, 2 );
WEIGHTED_ANS( ($popup72)->cmp, 2 );
WEIGHTED_ANS( ($ans7)->cmp, 4 );
WEIGHTED_ANS( ($popup81)->cmp, 1 );
WEIGHTED_ANS( ($popup08)->cmp, 2 );
WEIGHTED_ANS( ($popup82)->cmp, 2 );
WEIGHTED_ANS( ($ans8)->cmp, 4 );
WEIGHTED_ANS( ($popup91)->cmp, 1 );
WEIGHTED_ANS( ($popup09)->cmp, 2 );
WEIGHTED_ANS( ($popup92)->cmp, 2 );
WEIGHTED_ANS( ($ans9)->cmp, 5 );
WEIGHTED_ANS( ($popup101)->cmp, 1 );
WEIGHTED_ANS( ($popup010)->cmp, 2 );
WEIGHTED_ANS( ($popup102)->cmp, 2 );
WEIGHTED_ANS( ($ans10)->cmp, 4 );
WEIGHTED_ANS( ($popup111)->cmp, 1 );
WEIGHTED_ANS( ($popup011)->cmp, 2 );
WEIGHTED_ANS( ($popup112)->cmp, 2 );
WEIGHTED_ANS( ($ans11)->cmp, 4 );



ENDDOCUMENT();