Tricky Theoretical Probability Question

[Chrissy]

Hey

So, for a school assignment we had to create a carnival game and then calculate the empirical & theoretical probability of it. My game was called 'splat the rat;' basically, I put a computer mouse down a pipe and a contestant had to try and hit it when it came down the bottom. The empirical part was easy; according to it, there is a 47% chance that the mouse will be hit at the bottom. But I'm really struggling with the theoretical aspect; should I find out the average persons reflexes and then calculate the velocity of the mouse going down the pipe and then put them together somehow? If this is on the right track, then how would I find the velocity again? I haven't done science for two years

Many thanks!

 

[JeffM]

Hey

So, for a school assignment we had to create a carnival game and then calculate the empirical & theoretical probability of it. My game was called 'splat the rat;' basically, I put a computer mouse down a pipe and a contestant had to try and hit it when it came down the bottom. The empirical part was easy; according to it, there is a 47% chance that the mouse will be hit at the bottom. But I'm really struggling with the theoretical aspect; should I find out the average persons reflexes and then calculate the velocity of the mouse going down the pipe and then put them together somehow? If this is on the right track, then how would I find the velocity again? I haven't done science for two years

Many thanks!

Personally, I doubt it is possible to calculate a meaningful "theoretical" probability for this game because it is likely to be a computation dependent on, and perhaps senstive to, many variables: average exit velocity of mouse given deviations of pipe from perfect verticality, of average location of release of mouse relative to the center of the pipe, of weight of average mouse, of average coefficient of friction between mouse and pipe, average age of player attracted to the game, average reaction time given age of average player, average length of swing, average error in aim as a function of average exit velocity of mouse and age of average player, etc. There are probably more variables to be considered. In other words, I suspect that this particular game is not amenable to calculation from first principles, and empirical testing is the best that you can do.