A spider hunting a fly moves between locations 1 and 2 according to a 0.7 0.3 Markov chain with transition matrix starting in location 1. 0.3 0.7 The fly, unaware of the spider, starts in location 2 and moves according to a Markov chain with transition matrix 0.4 0.6 060.4

. The spider catches the fly and the hunt ends whenever they meet in the same location. 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 fly are at different locations. Obtain the transition matrix for this chain

(a) Find the probability that at time n the spider and fly are both at their initial locations

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