Simple Monty Hall

What is Simple Monty Hall?

This activity allows the user to simulate the standard Monty Hall Game.

The user chooses a door, and then another door is opened to reveal a stinking pig. The player must then decide to stick with the original choice or change.

This applet allows the user to experiment with conditional probability by choosing to stay or to switch doors. Conditional probability is the probability that an event will occur based on the outcome of the previous event. The particular "condition" is the event of opening a non-winning door based on which door is first picked. Based on the information the user just learned, he has a better chance of guessing the right door.

Probability began in the middle of the seventeenth century by a man named Pascal. One day a man proposed a question about gambling. His question was "If I play a game that I have eight rolls to roll a six and I fail the first three times, how much of my bet should I get back?" The game involved chance just as most of games do now, such as Monopoly and card games. Las Vegas is a city that is dominated by people that have invested in this field of mathematics. Today, probability has found its way into the fields of science, medicine, and statistics.

How Do I Use This Activity?

This activity allows the user to simulate the standard Monty Hall Game. The user chooses a door, and then another door is opened to reveal a stinking pig. The player must then decide to stick with the original choice or change.

Controls and Output

  • Observe three closed doors at the beginning of each round of the game:
  • Click on a door you want to pick. The selection sign will appear on the door you picked. Here the door on the left is selected:
  • Then one of the other two doors will open to reveal a pig.
  • Click on one of the remaining two doors to find out whether there is the grand prize or a pig behind it.
  • Click on the Let's do it again button to start a new game:
  • Observe the data for the games when you stayed with the original door:
  • Then observe the data for the games when you switched:
  • Click on the Reset stats button to reset all the data to zeros:

Description

This activity allows the user to simulate the standard Monty Hall Game. The user chooses a door, and then another door is opened to reveal a stinking pig. The player must then decide to stick with the original choice or change. This activity would work well in mixed ability groups of two to three for about fifteen to twenty minutes if you use the exploration questions and five to ten minutes otherwise.

Place in Mathematics Curriculum

This activity can be used to:

  • introduce the notions of chance and probability
  • motivate the notion of conditional probability
  • motivate the notion of random numbers

Standards Addressed

Grade 6

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 7

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 8

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 9

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability and counting techniques.

Grade 10

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability and counting techniques.

Seventh Grade

  • Statistics and Probability

    • Investigate chance processes and develop, use, and evaluate probability models.

Statistics and Probability

  • Conditional Probability and the Rules of Probability

    • Understand independence and conditional probability and use them to interpret data
    • Use the rules of probability to compute probabilities of compound events in a uniform probability model

  • Making Inferences and Justifying Conclusions

    • Understand and evaluate random processes underlying statistical experiments
    • Make inferences and justify conclusions from sample surveys, experiments, and observational studies

  • Using Probability to Make Decisions

    • Calculate expected values and use them to solve problems
    • Use probability to evaluate outcomes of decisions

Grades 9-12

  • Data Analysis and Probability

    • Develop and evaluate inferences and predictions that are based on data
    • Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
    • Understand and apply basic concepts of probability

Advanced Functions and Modeling

  • Data Analysis and Probability

    • Competency Goal 1: The learner will analyze data and apply probability concepts to solve problems.

AP Statistics

  • Data Analysis and Probability

    • Competency Goal 3: The learner will collect and analyze data to solve problems.

  • Number and Operations

    • Competency Goal 1: The learner will analyze univariate data to solve problems.

6th Grade

  • Data Analysis and Probability

    • The student will demonstrate through the mathematical processes an understanding of the relationships within one population or sample.

Textbooks Aligned

Book 1

  • Module 4 - Mind Games

    • Section 1: Experimental Probability
    • Section 1: Theoretical Probability

Be Prepared to

  • answer the question "What is Monty Hall?"
  • discuss probability and conditional probability