A bug lives on a number line. On its birthday, it must toss a coin and move positive one for heads or negative one for tails. The bug will die when it gets to either -2 or +2. How long will the bug live?
This is a classic problem in binomial probability so the students have many different points of entry. Some students play the game by hand ten or more times and find the average lifespan. This is generally around 3.6 years. These students also notice that the bug only dies on even turns.
Other students enter the problem through the use of Pascals Triangle. This allows students to calculate the number of pathways that would allow a bug to live and to compare this to the total possibilities. The students generally discover that the bug's liklihood of survival drops, by about half, every two turns.
Some students accept the challenge to write a computer program to run. I provide all of the students with TI Basic programs and Logo programs to help the students consider this problem. The programs are saved for the students on the school network. This year, however, was the first year that a student used a Scratch program.
The students learn Scratch through the Tech Savy kids program, run my Mrs. Hayes afterschool on Tuesdays. Here is a screen shot of the program and the code!
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