Where Probability Meets Geometry, the infinite may be infinitesimal
Here’s a simple problem that I think could bring up a number of good discussions. I’m not sure what grade level this is — I’m not sure geometric probability is ever taught, except to kids practicing for math contests. But hopefully some of the HS teachers out there will be able to tell me where this fits.
ABCD is a square with side length 10. P is a point chosen at random inside ABCD. What is the probability that P lies on one of the diagonals of ABCD?
If you teach probabilistic geometry, would you give students a problem like this? Do you think they would know how to solve it? Do you think they would really understand the solution, or feel that it is some artificial thing mathematicians do like setting 0! = 1?