# Classical Probability with a falling ball problem

1. Apr 10, 2013

### dweeegs

http://i793.photobucket.com/albums/yy215/dweeegs/probability_zps12a67dfb.png [Broken]

The picture shows everything needed.

This is a worksheet on the similarity of classical probability to the probability of finding a particle in a box (Schrodinger stuff etc)

Basically there's a ball falling down; it has a constant velocity on one platform and gains velocity going to another platform (where it's also constant). So two platforms and a ball has a different velocity on each (specifically the velocity on the second platform was found to be twice that on the first).

I found the probability that the ball will be found on each platform (pictured). The next question is giving me some problems since I haven't really taken stat in a while:

Use the answer I found in the picture to find P(x1,delta x), the probability of finding a ball between x1 and x1+delta x, where x1 is between 0 and L1 (the first platform), and delta x is small.

I'm clueless on how to approach this :/

The probability of two independent events occurring is the multiplication of those two probabilities, but I don't know how that would involve x1 or delta x, and it says to plot the probability vs x. But on second thought it might make sense because since the velocities are constant, the probability is constant.

It then goes on to ask about finding the probability between x1 and x1+(delta x)/2 and plot that as well, but I'm not sure how that would differ from the first question.

Am I on the right track? Any help?

Last edited by a moderator: May 6, 2017
2. Apr 10, 2013

### haruspex

I don't understand what the relationship is assumed to be between the velocity at a location and the probability of being there at an instant. you seem to be taking them as directly proportional - is that right? (Why?) Inversely proportional would be more intuitive.