Checkpoint 1.7.1.
Consider a standard die (a cube with six sides often used in games) and pick a desired side. Continue to roll the die until that side appears the first time and report the number of rolls that it took. Repeat this experiment 12 times and collect the various responses.
- Collect the response numbers on a number line.
- What would be the set of "possible" response numbers?
- Discuss whether you would ever get a response number of (say) 50 rolls.
- Would you expect any symmetries in general if this experiment were repeated a large number of times?