View Full Version : Expected Value Problem (not a poker problem)

10-09-2003, 04:59 AM
Here is a rather interesting problem I had to solve a week ago while helping a some people do some homework.

"Tom, who runs track, is preparing to run a n meter hurdle race. This race is made difficult by the fact the hurdles are placed at essentially random along the n meter race. Normally while running Tom moves at a rate of one meter per step. However when he encounters a hurdle, he must leap into the air, covering a distance of two meters in a single step. Jumping a hurdle is strenuous so until the hurdle is as close as possible, Tom will maintain 1 meter steps. At any point in the race (i.e. after any initial number of steps), either of two events may happen each with a certain probability.
1) Tom must clear a hurdle on his next step; this happens with probability p
2) Otherwise Tom is to run at his normal rate of 1 meter per step

Also If Tom has 1 meter left to run a hurdle will never appear.

What is the expected value of the number of steps Tom takes?"