Here's a very interesting problem sent in by Lee. Have fun playing with this.
Toby has a jar with one amoeba in it. Every minute, every amoeba turns into 0, 1, 2, or 3 amoebae with a probability of 1/4 for each case (dies, does nothing, splits into two, or splits into three). What is the probability that the amoeba population eventually dies out?If you're wondering, Lee's brother Chip created the image above. I'm guessing it has something to do with the solution.