A woman travels to work by bicycle 70% of the time and by scooter 30% of the time. If she uses her bicycle she is late 3% of the time but if she uses her scooter she is late only 2% of the time.

a. Find the probability that the woman is late for work on any particular day.

b. Given that the woman expects not to be late on approximately 223 days in a year, find the number of days in a year on which she works.