Marble Probability

Getting Started

The student is unable to determine the probability of most of the outcomes.

The student does not know how to represent or calculate probabilities. The student:

• Rounds each frequency to the next lowest multiple of 10 and writes these values as percents.
  
  
  
   
• Divides the total number of outcomes by the number of favorable outcomes (e.g., ).
  
  
  
   

How is probability determined?

How can you represent probability in fraction form? Should the total number of outcomes be in the numerator or denominator? Why?

If each outcome is equally likely, how should the frequencies of each outcome compare? How should the probabilities compare?

Review the meaning of probability and how it is calculated. Explain that the probability of an event is the number of outcomes favorable to that event compared to the total number of outcomes. Use a variety of manipulatives (e.g., coins, number cubes, and spinners) to demonstrate how probabilities are calculated. Clearly describe each possible outcome, the total number of outcomes, outcomes favorable to a particular event, and the number of outcomes favorable to that event. Guide the student to calculate specific probabilities and to write the probabilities in multiple forms: fraction, decimal, and percent. Remind the student that the probability of an event is a number between zero and one (or 0% and 100%). Consider implementing CPALMS Lesson Plan A Roll of the Dice (ID 34343) or Marble Mania (ID 4732), to help students understand probability of simple events.

Making Progress

The student is unable to determine whether the outcomes appear to be equally likely.

The student correctly records the probability of each outcome but:

• Says the outcomes appear equally likely because the probabilities are very similar.
  
  
  
   
• Says the outcomes are not equally likely because they are different or not exactly the same.
  
  
  
   

The student recognizes that the probabilities are not the same but does not understand the implications of this.

What does likely mean? What does equally likely mean?

Are all of the colors equally likely to be picked? Why or why not?

Are the frequencies of the outcomes close to what you expected?

What could cause the outcomes to be so different from what you expected?

Make explicit that equally likely does not mean that the outcomes will occur with precisely the same frequency in an experiment. Guide the student to compute the theoretical probabilities of selecting each color marble if the bag contains the same number of each color marble. Then have the student compare the experimental probabilities to the theoretical probabilities to determine if they are reasonably close. Explain to the student that some deviation from the theoretical probabilities will occur even when the bag contains the same number of each color marble. However, significant departures from these theoretical probabilities, as in this case, suggest that each color is not equally likely to be selected. Justify this conclusion by comparing the observed probabilities of purple, 0%, and yellow, 38%, to an expected outcome of 20% for each color.

Consider implementing CPALMS Lesson Plan M & M Candy: I Want Green (ID 7021), a lesson in which theoretical and experimental probabilities are compared. 

Got It

The student provides complete and correct responses to all components of the task.

The student accurately calculates the probability of each outcome in either fraction, decimal, or percent form.

The student says the outcomes are not equally likely because the probabilities are very different (e.g., yellow was picked much more than expected and purple was not picked at all). The student explains that there may not have been one of each marble in the bag since purple was never chosen and yellow was chosen about twice as often as blue, green, or red.

How many times would you have expected each color to be selected if the bag contained the same number of each color marble?

What can you guess about the number of purple marbles in the bag? How many of each color marble do you think is in the bag?

Ask the student to consider how different the probabilities could be in order for the student to conclude that the bag contained the same number of each color marble. Consider implementing MFAS task Number Cube to further assess the student’s understanding of this concept.