According to a consumer report, approximately 3% of New Zealanders bought a new vehicle in the past 12 months. The report also indicates that 10% commenced a new job in the same period. The report further reveals that in the past 12 months, 2% bought a new vehicle and commenced a new job. A New Zealander is randomly selected.

(a) What is the probability that in the past 12 months the individual has purchased a new vehicle or commenced a new job?

(b) What is the probability that in the past 12 months the individual has purchased a new vehicle or commenced a new job but not both?

(c) What is the probability that in the past 12 months the individual has neither bought a new vehicle nor commenced a new job?

(d) Why does the special law of addition not apply to this problem?