From past records, it is observed that in a typical year (365 days), air pollution

in a city was caused by excessive dust alone on 30 days, by car exhaust alone on 60 days,

and on 10 days the pollution was caused by both excessive dust and car exhaust. Assume

that they are the only two sources of air pollution and are statistically independent. The

probabilities of excessive dust and car exhaust are estimated to be 0.01 and 0.05 per day,

respectively.

(a) What is the probability that the city will have an air pollution problem on a given

day?

(b) What is the probability that the city will have an air pollution problem on a given day

due to dust? Due to car exhaust? Due to both dust and car exhaust?

(c) Suppose that on a particular day the air is polluted. What is the probability that it is

caused by car exhaust?