I agree that your agenda seems over ambitious. If you want to do probability, I would suggest warming up with the Buffon needle problem and then using Bertrand’s paradox as the main course. Monty Hall and St.Petersburg paradoxes are also good.
Buffon’s Needle will likely require more math than many highschool students even bright highschool students have. If they don’t have integration, Buffon’s Needle is tough.
I agree that your agenda seems over ambitious. If you want to do probability, I would suggest warming up with the Buffon needle problem and then using Bertrand’s paradox as the main course. Monty Hall and St.Petersburg paradoxes are also good.
Buffon’s Needle will likely require more math than many highschool students even bright highschool students have. If they don’t have integration, Buffon’s Needle is tough.
Hmmm. Maybe math is done more rigorously and less intuitively these days. When I was in high school, Buffon was done in three simple steps.
Change the length of needle and change the problem from probability of line-crossing to expected count of line-crossings.
What happens to the expected count if the needle is bent?
What happens if you bend a needle of length pi into a circle and drop it on a ruled sheet with spacing of 1 unit?
Yes, this is the beautiful conceptual solution to the problem, but it’s not universally known. I saw it in these two places:
http://blog.sigfpe.com/2009/10/buffons-needle-easy-way.html
http://golem.ph.utexas.edu/category/2010/03/a_perspective_on_higher_catego.html
Yes, that seems quite nice. I had not seen that approach before (or if I have have no recall of it).