########################################################################
## DESCRIPTION
## A WeBWorK problem that asks students construct a probability distribution and answer questions on it. 
## WeBWorK problem written by JoAnne Taormina, <joanne(dot)taormina(at)ncc(dot)edu>
## ENDDESCRIPTION
##
## KEYWORDS('probability distribution', 'discrete')
##
## Author('JoAnne Taormina')
## Institution('Nassau Community College')
########################################################################
DOCUMENT();
loadMacros(
"PGstandard.pl",
"MathObjects.pl",
"PGgraphmacros.pl",
"weightedGrader.pl",
);
TEXT(beginproblem());

# make sure we're in the context we want
Context("Numeric");

Context()->strings->add(yy=>{},yb=>{},yr=>{},by=>{},bb=>{},br=>{},ry=>{},rb=>{},rr=>{});

$outcomes = List(Compute("yy"),Compute("yb"),Compute("yr"),Compute("by"),Compute("bb"),Compute("br"),Compute("ry"),Compute("rb"),Compute("rr"));
$roots = List( -3, -2 );

# the table data
$table_start = begintable(2);
$table_row[0]  = row( "X", "P(X)");

for ( $i = 1; $i <=3; $i++ )
{
   $table_row[$i]  = row( ans_rule(5), ans_rule(5));
}

$table_end   = endtable();

$value_X_0 = Compute("0");
$value_X_1 = Compute("1");
$value_X_2 = Compute("2");
$prob_X_0 = Compute("4/9");
$prob_X_1 = Compute("4/9");
$prob_X_2 = Compute("1/9");
$ans_c = Compute("1/9");
$ans_d = Compute("5/9");
$ans_e = Compute("8/9");
$ans_f = Compute("4/9");
$ans_g = Compute("1/9");

Context()->texStrings;
BEGIN_TEXT
$BCENTER
\{ image( "spinner_image.png" , width=>250, height=>250) \}
$BR $BR

$ECENTER
$BR$BR
Consider spinning a three colored spinner like the one shown here.  Each color has the same portion of area. We’ll symbolize the color $BBOLD blue $EBOLD with the the letter $BBOLD b $EBOLD, the color $BBOLD red $EBOLD with the letter $BBOLD r $EBOLD, and the color $BBOLD yellow $EBOLD with the letter $BBOLD y $EBOLD.
$BR$BR
(a) On paper, construct a tree diagram for spinning the spinner $BBOLD twice. $EBOLD  
$BR$BR $BITALIC (Hint, there are 9 outcomes, and the order of the letters is important.) $EITALIC
$BR$BR
Write all 9 outcomes using the correct letters, separating each outcome with a comma “,”.  For example, you should type $BBOLD bb, br $EBOLD to indicate the outcomes $BBOLD “blue blue” $EBOLD and $BBOLD “blue red.” $EBOLD
$BR$BR
Outcomes = \{ ans_rule(40) \}
$BR
$PAR
(b) Construct a probability distribution table for the $BBOLD number of yellows $EBOLD in two spins of this 3-colored spinner.  Leave probabilities as fractions, e.g. 1/2 instead of 50%.
$BR$BR
$BCENTER

$table_start
$table_row[0]
$table_row[1]
$table_row[2]
$table_row[3]
$table_end

$ECENTER
$PAR
Use the probability distribution table in part (b) to answer the following questions:
$BR$BR
(c) What is the probability of getting 2 yellows in two spins of the spinner?  Answer as a fraction. \{ ans_rule(5) \}
$BR$BR
(d) What is the probability of getting $BBOLD $BITALIC at least 1 $EBOLD $EITALIC yellow in two spins of the spinner? Answer as a fraction. \{ ans_rule(5) \}

$BR$BR 
(e) What is the probability of getting $BBOLD $BITALIC at most 1 $EBOLD $EITALIC yellow in two spins of the spinner? Answer as a fraction. \{ ans_rule(5) \}

$BR$BR
(f) What is the probability of getting $BBOLD $BITALIC less than 1 $EBOLD $EITALIC yellow in two spins of the spinner? Answer as a fraction. \{ ans_rule(5) \}

$BR$BR
(g) What is the probability of getting $BBOLD $BITALIC more than 1 $EBOLD $EITALIC yellow in two spins of the spinner? Answer as a fraction. \{ ans_rule(5) \}

END_TEXT
Context()->normalStrings;

WEIGHTED_ANS( $value_X_0->cmp(),4 );
WEIGHTED_ANS( $prob_X_0->cmp(),6 );
WEIGHTED_ANS( $value_X_1->cmp(),4 );
WEIGHTED_ANS( $prob_X_1->cmp(),6 );
WEIGHTED_ANS( $value_X_2->cmp(),4 );
WEIGHTED_ANS( $prob_X_2->cmp(),6 );

WEIGHTED_ANS( $outcomes->cmp(),10 );

WEIGHTED_ANS( $ans_c->cmp(),8 );
WEIGHTED_ANS( $ans_d->cmp(),13 );
WEIGHTED_ANS( $ans_e->cmp(),13 );
WEIGHTED_ANS( $ans_f->cmp(),13 );
WEIGHTED_ANS( $ans_g->cmp(),13 );

ENDDOCUMENT();