Coin Toss

What is Coin Toss?

This activity allows the user to explore experimental probabilities through simulation of a coin toss.

There are many ways to look at the results of a probability experiment including lists, hash tables, counts of outcomes, ratios, percents, graphs, and more. In this activity you can view the results as a list, ratios and probabilities, and a table.

Closely tied to experimental probability is theoretical probability. The theoretical probability of an event is the ratio between the number of possible outcomes if a particular event compared to the total number of outcomes. With any one given coin toss, if the coin is fair, the probability of getting a head is 1/2. This is because a head occurs once on a coin and there are two equally likely possibilities.

A man named Pascal discovered probability in the middle of the seventeenth century. 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 explore experimental probabilities by simulating a coin toss.

Controls and Output

* Enter in the Number of Tosses to simulate and click the Toss 'em! button.

* The results of the coin toss will appear in the box at the bottom of the screen. You can view the results as a List, as a Table, or as Ratios. Simply depress the corresponding button to view the output in the particular form you want.

* Click the Clear Results button to begin a new experiment.

Description

This activity allows the user to explore experimental probabilities by simulating a coin toss. This activity would work well in groups of two for about ten minutes.

Place in Mathematics Curriculum

This activity can be used to:

  • introduce the notions of chance and probability
  • show the difference between experimental and theoretical probability
  • motivate the idea of sample size

Standards Addressed

Grade 3

  • Statistics and Probability

    • The student demonstrates a conceptual understanding of probability.

Grade 4

  • Statistics and Probability

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

Grade 5

  • Statistics and Probability

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

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.

Grade 3

  • Statistics, Data Analysis, and Probability

    • 1.0 Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions

Grade 4

  • Statistics, Data Analysis, and Probability

    • 2.0 Students make predictions for simple probability situations

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 3-5

  • Data Analysis and Probability

    • Develop and evaluate inferences and predictions that are based on data
    • Understand and apply basic concepts of probability

Grades 6-8

  • Data Analysis and Probability

    • Understand and apply basic concepts of probability

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

Grade 6

  • Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

    • COMPETENCY GOAL 4: The learner will understand and determine probabilities.

Advanced Functions and Modeling

  • Data Analysis and Probability

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

Integrated Mathematics

  • Data Analysis and Probability

    • Competency Goal 3: 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.

4th Grade

  • Data Analysis and Probability

    • Standard 4-6: The student will demonstrate through the mathematical processes an understanding of the impact of data-collection methods, the appropriate graph for categorical or numerical data, and the analysis of possible outcomes for a simple event.

5th Grade

  • Data Analysis & Probability

    • The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

3rd Grade

  • Data Analysis

    • Content Standard 5.0 The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

4th Grade

  • Data Analysis & Probability

    • The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

Grade 5

  • Probability and Statistics

    • 12. The student describes and predicts the results of a probability experiment.

3rd Grade

  • Probability and Statistics

    • 3.23 The student will investigate and describe the concept of probability as chance and list possible results of a given situation.

Be Prepared to

  • Discuss the difference between theoretical and experimental probability
  • Discuss why the experimental probability of getting heads (or tails) is not one half, especiallywith a small sample.