Elizabeth takes the bus with probability 0.7 and the subway with probability 0.3. Elizabeth is late 45% of the time when they take the bus but only 5% of the time when they take the subway. What is the probability Elizabeth is late for work? (Please answer with a value between 0 and 1. For example 0.24 instead of 24%.) Give an exact answer (explained) if possible, otherwise 3 decimal accuracy please.