Saw a great problem from the 2009 AMC 10 last night:
Here’s the problem:
3 verticies of a cube are chosen at random. What is the probability that the plane formed by those three verticies contains points inside of the cube?
This is a great problem (and a challenging one, too). My older son took a few missteps walking through it, but our whole conversation about the problem this morning was great.
here’s the first part:
In the second part he takes a little misstep, but hopefully the mistake turned into a good learning opportunity:
Now we back up to where the misstep happened and try to get to the end of the problem: