unaware of the spider, starts in location

unaware
of the spider, starts in location 2 and moves according Markov chain
with transition matrix . 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 it the spider and fly are both at
their initial locations

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

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