BasicProbabilityConcepts_GuidedProblem1.pg

## DESCRIPTION
## WeBWorK Guided Problems Project — Sample Spaces & Events (Guided / Scaffolded)
## ENDDESCRIPTION
##
## Institution(Dawson College)
## Author(Mehdi Moodi)
## DBsubject(Statistics)
## DBchapter(Probability)
## DBsection(Sample Spaces and Events)
## Level(2)
## KEYWORDS('probability','sample space','event','random experiment','trial')

DOCUMENT();

loadMacros(
  "PGstandard.pl",
  "PGanswermacros.pl",
  "MathObjects.pl",
  "contextString.pl",
  "scaffold.pl",
);

TEXT(beginproblem());

# ----------------------------------------------------------------
# PILOT: usefulness rating toggle (ACTIVE)
# ----------------------------------------------------------------
$ENABLE_GP_RATING = 1;   # set to 0 to hide/remove the rating step

# =======================================================
# Evaluators for set-entry (order doesn't matter)
# =======================================================
Context("String");

# Critical: allow comma-separated lists of strings to be parsed as a List
Context()->operators->redefine(',', using => ',');

# Allowed outcomes
Context()->strings->add(
  "WW" => {},
  "WB" => {},
  "BW" => {},
  "BB" => {},
);

$correctS = List( String("WW"), String("WB"), String("BW"), String("BB") );
$correctE = List( String("WB"), String("BW") );

# =======================================================
# Rating evaluator (integer 1–5)
# =======================================================
Context("Numeric");
$cmp_rating = Real(1)->cmp(
  checker => sub {
    my ($correct, $student, $ansHash) = @_;
    return 0 unless defined $student;
    my $v = $student->value;
    return 0 unless defined $v;
    return 0 unless $v == int($v);
    return ($v >= 1 && $v <= 5) ? 1 : 0;
  }
);

# Switch back to String for the rest of the problem display/inputs
Context("String");

# =======================================================
# Scaffold
# =======================================================
Scaffold::Begin(
  numbered => 1,
  can_open => "when_previous_correct",
  is_open  => "correct_or_first_incorrect",
  hardcopy_is_open => "always",
);


# -------------------------------------------------------
Section::Begin("Problem Statement");
BEGIN_TEXT
A bag contains 12 white marbles and 8 black marbles.
$PAR
You will draw two marbles, one after the other, with replacement.
END_TEXT
Section::End();

# -------------------------------------------------------
Section::Begin("Build the definitions");
BEGIN_TEXT
For each blank, choose the best option by typing its letter (A, B, or C).
$PAR

Build the definition of a <b>random experiment</b>:
$BR
A random experiment in probability is a (1) ____ procedure or process that can be (2) ____,
has (3) ____ possible outcomes, but whose specific result cannot be predicted with (4) ____ beforehand,
though the set of all possible outcomes (the (5) ____) is known.
$PAR

(1)
$BR
A) random   B) well-defined   C) unclear
$BR
Answer: \{ ans_rule(2) \}
$PAR

(2)
$BR
A) ignored   B) repeated   C) guessed
$BR
Answer: \{ ans_rule(2) \}
$PAR

(3)
$BR
A) one   B) none   C) multiple
$BR
Answer: \{ ans_rule(2) \}
$PAR

(4)
$BR
A) certainty   B) luck   C) noise
$BR
Answer: \{ ans_rule(2) \}
$PAR

(5)
$BR
A) trial   B) sample space   C) event
$BR
Answer: \{ ans_rule(2) \}
$PAR

Each performance of the experiment is called a (6) ____.
$BR
A) event   B) trial   C) outcome
$BR
Answer: \{ ans_rule(2) \}
$PAR

The sample space is the (7) ____ of all possible outcomes.
$BR
A) set   B) formula   C) number
$BR
Answer: \{ ans_rule(2) \}
$PAR

An event is a (8) ____ of the sample space.
$BR
A) average   B) equation   C) subset
$BR
Answer: \{ ans_rule(2) \}
$PAR

We say an event (9) ____ when the observed outcome is in that event.
$BR
A) occurred   B) repeated   C) vanished
$BR
Answer: \{ ans_rule(2) \}
END_TEXT

ANS( str_cmp("B") ); # (1) well-defined
ANS( str_cmp("B") ); # (2) repeated
ANS( str_cmp("C") ); # (3) multiple
ANS( str_cmp("A") ); # (4) certainty
ANS( str_cmp("B") ); # (5) sample space
ANS( str_cmp("B") ); # (6) trial
ANS( str_cmp("A") ); # (7) set
ANS( str_cmp("C") ); # (8) subset
ANS( str_cmp("A") ); # (9) occurred

Section::End();

# -------------------------------------------------------
Section::Begin("Identify the random experiment");
BEGIN_TEXT
Which option correctly describes the random experiment for this situation?
$PAR
A) Draw a marble, replace it, draw again, and record the ordered pair of colors (first, second).
$BR
B) Draw two marbles without replacement and record only the final color.
$BR
C) Shake the bag and predict the color without drawing.
$PAR
Answer (A/B/C): \{ ans_rule(2) \}
END_TEXT

ANS( str_cmp("A") );

Section::End();

# -------------------------------------------------------
Section::Begin("Construct the sample space");
BEGIN_TEXT
We will use W for white and B for black.
$PAR
Example: First draw is white and second draw is black is written as WB.
$PAR
Enter the sample space outcomes as a comma-separated list. Order does not matter.
$PAR
S = { \{ ans_rule(30) \} }
END_TEXT

ANS( $correctS->cmp(ignoreOrder => 1) );

Section::End();

# -------------------------------------------------------
Section::Begin("Define an event");
BEGIN_TEXT
Let E be the event: "Exactly one black marble is drawn."
$PAR
Enter the outcomes in E as a comma-separated list. Order does not matter.
$PAR
E = { \{ ans_rule(20) \} }
END_TEXT

ANS( $correctE->cmp(ignoreOrder => 1) );

Section::End();

# -------------------------------------------------------
Section::Begin("Which event occurred?");
BEGIN_TEXT
Suppose the observed outcome is WB.
$PAR
Which one of the events below occurred?
$PAR

A) At least one white marble was drawn.
$BR
Set form: { WW, WB, BW }
$PAR

B) Both marbles drawn were black.
$BR
Set form: { BB }
$PAR

C) Both marbles drawn were white.
$BR
Set form: { WW }
$PAR

D) The first draw was black.
$BR
Set form: { BW, BB }
$PAR

Answer (A/B/C/D): \{ ans_rule(2) \}
END_TEXT

ANS( str_cmp("A") );

Section::End();

# ----------------------------------------------------------------
# PILOT RATING (ACTIVE)
# ----------------------------------------------------------------
if ($ENABLE_GP_RATING) {

  Section::Begin("Feedback");
  BEGIN_TEXT
Rate the usefulness of this guided problem on a scale from 1 to 5.
$PAR
(1 = not useful, 2 = slightly useful, 3 = useful, 4 = very useful, 5 = extremely useful)
$BR
Note: Consider using the Email Instructor button below to suggest improvements.
$PAR
Rating: \{ ans_rule(6) \}
END_TEXT

  Context("Numeric");
  ANS($cmp_rating);
  Context("String");

  Section::End();
}

Scaffold::End();

ENDDOCUMENT();