An ant is walking on the squares of a 5x5 grid - it starts in the center square.
Each second, it will choose (with equal probability) to do one of the following:
- Move north one square
- Move south one square
- Move east one square
- Move west one square
- Do not move
If it cannot perform the action it has decided on (move west while on the west edge, for example), it sits in place.
After one second, it has a 20% chance of being in the center, and a 20% chance of being in each adjacent square. (and a 0% chance of being in any other square on the board).
- What is the probability that the ant is on the center square after 15 seconds?
- What is the probability that the ant is on one of the outermost squares after 1 hour?
Any suggestions? In the first question, I don't know how to enumerate all the possible routes that finish on the middle square after 15 moves and divide them by the total number of possible routes. In the second one, I'm completely lost.
Thanks for your help :-)