Question

A man either drives his car or takes a bus to work each day. Suppose he never
takes the bus two days in a row, but if he drives to work then the next day he is
just likely to drive again as he is to take the bus. At the first day, he tosses a coin
and if tail comes then he takes a bus to work. Otherwise he drives to work. Find
the transition probability matrix. Also find the probability that he will use the bus
to go to work after four days.

Answer 1

Answer:

He never goes 2 days in a row by train but if he drives one day, then the next day he is just as likely to drive again as he is to travel by train.