A man either drives his car to work or catches a train. Assume that he never takes the train two days in a row but if he drives to work, than the next day he is just as likely to drive again as he is to catch the train. Evaluate (a) the probability that he drives to work after (i) 2 days (ii) a long time, (b) the probability that he drives to work after (i) 2 days, (ii) a long time if on the first day of work he tosses a fair die and drives to work only if a 2 appears.