Here's my attempt at the challenge. OK, it's probably overkill but I had fun doing it. :-)

//create 2D array [question, answer, guessedCorrectly, #times guessed]
var quizdata = [];

//populate quizdata and prompt user to play or quit
setupQuiz();

function print(message) {
  document.writeln(message + "<br />");
}

function msgAsk(strMessage) {
   return confirm(strMessage);
};//msgAsk

function displayStats() {
  var strStats = "";

  for (var i = 0; i < quizdata.length; i++) {
     strStats = "You guessed question #" + (i + 1) 
     + " " + ((quizdata[i][2]) ? "correctly" : "incorrectly") 
     + " after " + parseInt(quizdata[i][3]) + " attempts.";
     print(strStats);
  }//(var i = 0; i < quizdata.length; i++)



};//displayStats()


function getCorrectAnswerCount() {
  /*increment count of correctly answered questions when
  element 2 of associated array is true */
  var count = 0;
  for (var i = 0; i < quizdata.length; i++) {
     if (quizdata[i][2]) {
       count++;
     }//if (quizdata[i][2])
  }//for
  return count;
};//getCorrectAnswerCount()

function setupQuiz() {
  //clear array of any data
  quizdata.length = 0;

  //insert an array consisting of a question and then answer, guessedCorrectly and timesGuessed
  //guessedCorrectly default is false; timesGuessed default is 0
  var strQuestion = "";
  strQuestion = "How many planets are there in the solar system?";
  strAnswer = "8";
  quizdata.push([strQuestion, strAnswer, false, 0]);

  strQuestion = "What is the most prevalent element in the earth's atmosphere?";
  strAnswer = "Nitrogen";
  quizdata.push([strQuestion, strAnswer, false, 0]);

  strQuestion = "Is Python strongly typed?";
  strAnswer = "No";
  quizdata.push([strQuestion, strAnswer, false, 0]);

  //welcome the user to the quiz

  print("Welcome to the Quiz Game!");
  print("You have 10 tries to answer three questions.");
  print("You can type STOP! at any prompt to end the game immediately.");

  if (!msgAsk("Ready to play?")) {
     alert("Thank you!");
    return;
  } else {
    runQuiz();
  }
};//setupQuiz()

function askQuestion() {
    //display first incorrectly or unaswered question available.
     //don't display correctly answered question
     //check user input aganst element 1 of array
     //return true if answered correctly; otherwise return false
     var currentQuestion = 0; //index of next incorrectly answered question 

     //get index of next incorrectly answered question attempted no more than three times
     for (var i = 0; i < quizdata.length; i++) {
        if (!quizdata[i][2] && quizdata[i][3] < 3) {
          currentQuestion = i;
          break;
        }//if (!quizdata[i][2])
     }//(var i = 0; i < quizdata.length; i++)

    while (quizdata[currentQuestion][3] < 3) {
      //increment count of attempts to answer this question
      quizdata[currentQuestion][3]++;
     if (prompt(quizdata[currentQuestion][0]).toLowerCase() === quizdata[currentQuestion][1].toLowerCase()) {
       //mark question as correctly answered
       quizdata[currentQuestion][2] = true;
       alert("Great! You answered the question correctly!");
       break;
     } else {
       alert("Oops! That is not the correct answer. " + (3 - quizdata[currentQuestion][3]) + " tries remaining");
       //ask again until timesGuessed >= 3
     }//if (prompt(quizdata[currentQuestion][0]) === quizdata[currentQuestion][1].toLowerCase())
    }//while (quizdata[currentQuestion][3] <= 3) 
    return;
};//askQuestion()


function runQuiz () {
  /*run while loop until one of the following is true:
   1) all three questions have been answered coreectly 
   2) user inputs "STOP!"
   3) maxTries is exceeded */

   var maxTries = 10;
   var tryCount = 0;

   while (true) {

      if (tryCount < maxTries) {
         tryCount++;
      } else {
         alert("GAME OVER!");
         break;
      }//if (tryCount < maxTries)

     //check number of correctly answered questions
     if (getCorrectAnswerCount() === 3) {
        alert("You won the game by answering all three questions correctly!\nThank you for playing!");
       break;
     }//if (getCorrectAnswerCount() === 3) 

     askQuestion()

   }//while

  //let user know how well he/she did
  displayStats();
  return;

};//runQuiz()