A mouse has 3 rooms to go into.

If it goes into room 1, it will find the cheese after 3 minutes.

If it goes into room 2, it will look for cheese for 4 minutes, won't find it, and will go out.

If it goes into room 3, it will look for cheese for 5 minutes, won't find it, and will go out.

The mouse will not remember that it was in rooms 2 and 3 after it goes out of them, and it will continue going in and out until it finds the cheese. (It can go into the same room again and again.)

What is the average time for the mouse to find the cheese?

Assuming the mouse chooses rooms at random, the average time T = 3 + 2/3(T + 9/2) or T = 18 minutes.

Posted by xdog on 2008-09-11 12:17:51