## 35. Being Late for Work

Maurice goes to work either by his own car (and then due to traffic jams, he is late half of the time), or by subway (and then he is late only one time out of four). If on any given day Maurice arrives at work on time, he always uses the same mode of transport the next day as he did the previous day, but if he is late for work, he definitely changes his mode of transport the next day. Knowing all this, how likely is it that Maurice will be late for work when he goes there for the 467th time?