What are the odds in Russian roulette? Suppose two bullets are placed adjacent to each other and a single player is going to pull the trigger twice. Between trigger pulls, should the player spin the chamber? Would that change if the two bullets were not placed next to each other and instead placed randomly? These are the questions explored in this video. You should watch the video, then relay the explanations to your students. Before attempting this challenge, students should know how to compute probabilities for sequences of events. They should also know how to compute weighted probabilities.
Next, relay the first game from this video, then ask them for the probability that Edison wins. Then modify the problem, as seen in the video, and ask again.
Concude by giving your students this challenge:
Putting Two and Two Together by NRICH: Because NRICH states this problem is suitable for 7-11 years olds, but it references equilateral triangles and isosceles triangles, which are a grade 5 topic, these questions might be too easy for a 5th grader. What follows is how I would make the problem more difficult, for the students who aren't feeling challenged. There is only 1 free polyiamond for \(n = 2,\) but what about \(n = 3?\) 4? 5? 6? Drawings can be found here. The number of free polyabolos, for \(n \le 4,\) is also reasonable. I haven't found drawings for this, only the number of shapes for each \(n,\) which is here. For polydrafters, \(n \le 5\) is reasonable. Again, I couldn't find a drawing, but there's a listing of the number of shapes here.
TODO: Drawings for polyiamonds \(n \le 4\) and polydrafters \(n \le 5.\)