A spider hunting a y moves between locations 1 and 2 according to a Markov chain with transition matrix P1 starting in location 1. The y, unaware of the spider, starts in location 2 and moves according to a Markov chain with transition matrix P2, where P1 =" .7 .3 .3 .7 # ,P2 =" .4 .6 .6 .4 #

The spider catches the y and the hunt ends whenever they meet in the same location. (i) (1 pts.

Show that the progress of the hunt, except for knowing the location where it ends, can be described by a three-state Markov chain where one absorbing state represents hunt ended and the other two that the spider and the y are at dierent locations. Obtain the transition matrix for this chain.

(ii) What is the average duration of the hunt?