Summary
This activity poses a fun probability problem concerning changing odds.
Materials
- One box per group of four students
- Three counters (one blue and two red) per group of four students
- Paper
- Pencil
Additional Resource
1000 Play Thinks: Puzzles, Paradoxes, Illusions & Games by Ivan
Muscovich (Workman Publishing).
Background for Teachers
In the following experiment, it would appear that the chances of a red counter
remaining in the box are 50%. However, there are actually three (not two) equally
possible states.
- The initial red counter was drawn, leaving the added red counter.
- The added red counter was taken, leaving the initial red counter.
- The added red counter was taken, leaving the blue counter.
Intended Learning Outcomes
2. Become mathematical problem solvers.
Instructional Procedures
Invitation to Learn
The Sock Problem
Instructional Procedures
- Hold up the box and explain that it contains either a red or a blue counter.
- Add a red counter, so the box now contains two counters.
- Ask the question, “If I pull out a red counter, what is the probability
that the remaining counter is also red?”
- Pass out materials to teams.
- Teams will conduct a series of experiments (at least 10).
- Teams will determine an appropriate format for displaying results (e.g.,
bar graphs, line graphs).
- Have the teams share their results with the class and propose a reason
for these results.
Extensions
Possible Extensions/Adaptations
Add more counters to the bag. Does it change the odds? How so?
Homework & Family Connections
Challenge students to conduct the same experiment with their families using
materials commonly found at home.
Assessment Plan
Have students design and complete a probability problem concerning changing
odds.
Created: 09/16/2003
Updated: 02/04/2018
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