Game of Chance PROJECT OVERVIEW: LOW-TECH PROBABILITY PRIMER Build a low-tech Galton board to help visualize probability (chance). Then, expand your exploration by removing or adding pegs to create different probability curves. PROJECT CATEGORY: Quantum DIFFICULTY LEVEL: Intermediate TIME RANGE: 45 - 90 minutes GROUP SIZE: 2 - 4 ESSENTIAL SKILLS AND MINDSETS: Iteration Prototyping Simple Machines Collaboration Embracing Your Mistakes FUTURE SKILLS Copyright © 2021 Design Case, LLC 1 QUANTUM COMPUTING Dream It! In this project, you will get hands-on with probability by building a device of chance that sorts round beads into a binomial distribution curve (also called a bell curve). You will not know for certain where each bead will end up, but you will always get a predictable curve. This is due to the probability (chance) of each bead bouncing left or right while traveling down your device. (For reference, this tool is called a Galton Board or bean counting device.) You can learn more about its unique names later on. 1. To start, watch the Galton Board Introduction Video and the Quantum Probability Videos to learn more about probability— including how it relates to quantum computing. [:05] 2. Now, read the Explore More: The Magic Behind Pascal’s Triangle section to get a better understanding of binomial distributions and the math behind a Galton board. [:05] EXPLORE MORE: THE MAGIC BEHIND PASCAL’S TRIANGLE? It’s amazing how you can use a simple idea like Pascal’s Triangle to solve complicated problems such as probability and advanced mathematics. What does Pascal’s Triangle look like? Here’s how it works: The top of the triangle is always 1. The second row below it is always (1, 1). Remember that the third row—and every other row—starts with 1 as well. To calculate the next number, you simply add the two numbers from the top row starting from the left (1 + 1 = 2). When all the numbers from the top row have been added, you will end with a 1. This means the second row becomes (1, 2, 1). From there, you will want to do the same thing for the third row so that your triangle looks like: (1, (1+2), (2+1), 1) or (1, 3, 3, 1) Then, simply continue. The bigger you make the triangle, the more problems you can solve. DID YOU KNOW: Lots of things in nature follow a normal (or binomial) distribution: People’s heights, shoe sizes, etc. What else can you think of that might follow a normal distribution? AT-HOME SUBSTITUTIONS: In a pinch, you can use a cardboard box instead of foam core for the back of the Galton board (thick foam is best for larger boards). Or, if you really want a fun challenge, try to make a Galton board out of LEGOs—using the round “dots” instead of marbles or beads! TOOLS AND MATERIALS: Low-Tech Galton Board: • Printed Galton board templates tiny.cc/galtontemplates • Pencils, bamboo skewers, nails, pushpins, etc. (50 total) • Recycled materials • Hard foam or foam core sheet (8.5 inches x 11 inches or larger) • Marbles or beads of various sizes (1/4 inch or 6mm work best) • Large tongue depressors MATERIAL PURCHASE LINK: http://tiny.cc/Intelbuylist PROJECT INTRO VIDEO: • What’s a Galton Board? http://tiny.cc/galtonboard QUANTUM PROBABILITY VIDEO: • Galton Explained http://tiny.cc/galtonexplained Copyright © 2021 Design Case, LLC 2 QUANTUM COMPUTING 3. Design your Galton board: Now it is time to design your board! Use the Think About It section to guide your ideas. Then, when you’re ready, jot down the answers to each question. [:05] THINK ABOUT IT Your end goal is to