I liked your solution to my word triple problem, but unfortunately the arrays are non-responsive as I have entered them.

Can you see any problems? I think I entered your arrays as given...

Thanks, for any help.

# DESCRIPTION Function translations

# Translate descriptions of critical points and function

# into correct notation.

# WeBWorK problem written by TimPayer <tsp1@humboldt.edu>

# ENDDESCRIPTION

## DBsubject(Probability)

## DBchapter(Random variables)

## DBsection(Expectation)

## Institution(Humboldt State University)

## Author(Tim Payer)

## KEYWORDS(probability, translate, notation)

DOCUMENT();

loadMacros(

"PGstandard.pl",

"PGunion.pl",

"MathObjects.pl",

"parserPopUp.pl",

"PGML.pl",

"PGcourse.pl",

);

#Text(beginproblem()); #uncomment

install_problem_grader(~~&std_problem_grader);

$showPartialCorrectAnswers = 1;

Context("Numeric");

# create three arrays of the same length "in parallel"

@bird = ('goose','crow','starling');

@birds = ('geese','crows','starlings');

@flock = ('gaggle','murder','murmuring');

$i = random(0, 2, 1); # choose an array index at random

$popup1 = PopUp(

["probability notation", "P(V)", "P(N)", "P(VV)", "P(NN)", "P(VN)", "P(NV)",

"P(VN U NN)", "P(NV U NN)", "P(VN \[\cap \] NN)", "P(NV \[\cap \] NN)",

"P(VN \[\cap \] NV U NN)", "P(VN U NV \[\cap \] NN)", "P(VN U NV U VV)",

"P(VN \[\cap \] NV \[\cap \] NN)", "P(NN \[\cap \] NV U VN)", "P(NN U NV \[\cap \] VV)",

"P(NN \[\cap \] NV \[\cap \] VV)","P(VN \[\cap \] NV) + P(NN)", "P(VN \[\times \] NV) + P(NN)",

"P(VN \[\cap \] NN) + P(NV \[\cap \] NN)",], "P(VV)");

$popup2 = PopUp(

["probability notation", "P(V)", "P(N)", "P(VV)", "P(NN)", "P(VN)", "P(NV)",

"P(VN U NN)", "P(NV U NN)", "P(VN \[\cap \] NN)", "P(NV \[\cap \] NN)",

"P(VN \[\cap \] NV U NN)", "P(VN U NV \[\cap \] NN)", "P(VN U NV U VV)",

"P(VN \[\cap \] NV \[ \cap \] NN)", "P(NN \[\cap \] NV U VN)", "P(NN U NV \[\cap \] VV)",

"P(NN \[\cap \] NV \[\cap \] VV)","P(VN \[\cap \] NV) + P(NN)", "P(VN \[\times \] NV) + P(NN)",

"P(VN \[\cap \] NN) + P(NV \[\cap \] NN)",], "P(VN U NV U VV)");

BEGIN_PGML

1. A flock of [$birds[$i] ] is described as a [@flock[$i] ] of [$birds[$i] ].

Consider the case where (percent)% of a [@flock[$i] ] of [$birds[$i] ] carry a bird flu virus, and that two [$birds[$i]] are drawn at random from the [@flock[$i] ], find the following probabilities given the following variable declarations:

Let V = Event that a [$bird[$i] ] has the bird flu virus.

Let N = Event that a [$bird[$i] ] does not have the bird flu virus.

1a.) What is the probability of randomly drawing two [$birds[$i] ] that both have the bird flu virus? Choose the correct probability notation below and then calculate its associated probability with fourth decimal accuracy.

[___]{$popup1} =

1b.) What is the probability of randomly drawing two [$birds[$i] ] such that at least one [$bird[$i]] has the bird flu virus? Choose the correct probability notation below and then calculate its associated probability with fourth decimal accuracy.

[___]{$popup2} =

END_PGML

BEGIN_PGML_SOLUTION

The correct answers are:

END_PGML_SOLUTION

ENDDOCUMENT();