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Probability

The probability lessons provide experiments dealing with real world examples. Students can run examples to measure probability experimentally. The activities on probability are interactive, holding the interests of the students through hands-on activities. The students become able to find probability through modeling. Discussion topics and questions are provided for each lesson.

Probability Lessons
  1. Probability and Sports
    This lesson asks students to gather some sports statistics involving probability using the Internet as a resource. Statistics and probability concepts will arise such as what statistics are reliable.
  2. Ideas that Lead to Probability
    Basic ideas of probability theory are introduced in this lesson through the use of common experiences and intuitive thinking. Examples are shown with die and other common objects that illustrate probability.
    Related Activity: The Racing Game With One Die
  3. Unexpected Answers
    This lesson provides examples of unexpected answers of tricky probability questions. The lesson shows care should be taken when using probability. This includes games, which may seem fair but are not.
    Related Activities: Crazy Choices Game, Two Colors Applet, Monty Hall, Three Doors, and Monty Hall
  4. Introduction to the Concept of Probability
    This lesson introduces the basic set operations that are useful in solving probability problems that involve counting outcomes. This material is the basis of the so-called naive probability theory, which is built upon intuitive and experimental knowledge. Students will learn about outcomes and how to calculate experimental probability.
    Related Activity: Crazy Choices Game
  5. Probability and Geometry
    This lesson connects probability with geometry. The ideas of probability are extended from a counting sense to a visual representation through geometric proportions.
    Related Activities: Spinner and Adjustable Spinner
  6. Conditional Probability and Probability of Simultaneous Events
    This lesson involves estimation problems with unexpected and counterintuitive experimental results. This fact leads to a further exploration using mathematics to solve problems. The lesson is focused on conditional probability and the probability of simultaneous events.
    Related Activities: Racing Game with One Die, Two Colors Applet, and Monty Hall, Three Doors
  7. From Probability to Combinatorics and Number Theory
    This lesson focuses on data structures and their applications to probability theory. This includes using division to solve probability problems and using tables and trees as data structures for probability.
    Related Activities: Racing Game with Two Dice and Dice Table
  8. Expected Value
    This lesson investigates the definition and formula of expected value. The idea of payoff is introduced.
    Related Activities: Fire!! Stock Exchange Game
  9. Fire!, Probability, and Chaos
    This lesson utilizes concepts of probability, graphing and graph interpretation, mean, and variance in analyzing a simulation of a forest fire.
    Related Activity: Simple Plot
  10. The Bell Curve
    This lesson introduces the concepts of the normal curve, skewness and the standard deviation. The controversy over the 1994 book is also examined.
    Related Activities: The Normal Distribution and Skewness
Probability Activities
  1. Racing Game With One Die
    In this activity, two players each roll a die and, depending on the parameters, one player moves forward. The adjustable parameters include: which player gets to move for each number and how many steps to the finish line.
  2. Crazy Choices Game
    This activity involves three players who play games of chance using dice, cards, spinners or coin tosses. In these games, the students compare theoretical and experimental probabilities. The number of trials is adjustable.
  3. Two Colors Applet
    In this activity three boxes each contain two balls. Three of the balls are red and three are green. The balls are shuffled each trial and the probability of the colors is recorded. Students can adjust the number of trials to see what happens to the experimental probability over a large number of trials.
  4. Monty Hall, Three Doors
    Students choose one of three doors to experimentally determine the odds of winning the grand prize behind one of the doors in this activity, similar to the TV program "Let's Make a Deal." The students choose to stay or switch between the two remaining doors.
  5. Monty Hall
    This activity involves running a simulation to mimic the simple monty hall activity with multiple trials. Students can adjust the number of doors, number of trials, and staying or switching between the remaining doors.
  6. Spinner
    In this activity, students can create a game spinner with one to twelve sectors to look at experimental and theoretical probabilities. The number of sectors and the number of trials are adjustable.
  7. Adjustable Spinner
    Students can create a game spinner with variable sized sectors in this activity. They are able to look at experimental and theoretical probabilities for this spinner. The sizes of sectors, number of sectors, and number of trials are adjustable.
  8. Racing Game With Two Die
    This activity is a race between players using 2 dice. Players are assigned lucky numbers, which if rolled moves the player forward. Students can choose that the lucky player moves one step to the finish, or everybody moves one step and the lucky player moves two steps to the finish. Also the number of players, number of trials and length of the race can all be changed.
  9. Dice Table
    In this activity, students experiment with the outcome distribution for a roll of two dice by playing a dice throwing game. Students set which player wins on which rolls.
  10. Fire!!
    This activity is a simulation of how a fire will spread through a stand of trees. The activity teaches about probability and chaos. The student can choose the probability that a tree will catches fire if its neighbor is on fire.
  11. Stock Exchange Game
    This activity is a game in which the payoff is earnings from stocks. Students learn about expected value and payoff for an event that will occur with a known probability. They can adjust the probability of receiving cash, cash amounts, and the number of trials.
  12. Simple Plot
    This graphing activity allows students to plot ordered pairs of numbers, either as a scatter plot or with the dots connected.
  13. The Normal Distribution
    In this activity, students can change the standard deviation of the graphed normal distribution to create a new distribution. They are also able to change the number of trials and the class intervals. This statistical graphing program allows students to observe properties like how well the histogram fits the curve and how areas under the curve correspond to the probability that a number is selected.
  14. Skewness
    In this statistical activity, students can change the median standard deviation of the graphed normal distribution to create a skewed distribution. Students then are able to observe properties like what it means for the mean, median, and mode to be different. The median, standard deviation, number of trials, and class intervals be adjusted.
  15. Boxplot
    This activity allows students to create boxplots which use the median in calculating the interquartile ranges for either builtin or user-specified data as well as experiment with outliers. The students can enter different data.
  16. Bar Graph
    This activity enables students to enter data to create a bar graph, then manipulate the graph's maximum and minimum values. The students can enter different data.
  17. Stem-and-Leaf Plotter
    In this activity, students view stem-and-leaf plots of their data, and then get to practice finding means, medians and modes. The students can enter different data.
  18. Histogram
    In this activity, students can view histograms for either built-in or user-specified data, and experiment with how the size of the class intervals influences the perceptions. They can change the data sets and class sizes.
  19. Circle Graph
    This activity allows students to enter data categories and the value of each category to create a circle graph. Similar to "Pie Chart" but the user can define the data set.
  20. Plop It!
    In this activity, students click to build dot plots of data and view how the mean, median, and mode change as numbers are added to the plot. Students can adjust the range for observations.
  21. Marbles
    Students learn about sampling with and without replacement by modeling drawing marbles from a bag in this activity. The number and color of marbles in the bag and the replacement rule are adjustable.

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