Air pollution in a city is caused by the following four sources: vehicle exhaust (V), industrial exhaust (I), dust (D), and pollen from plants and trees (T). On a particular day, the likelihood of air pollution caused by these sources is 4:3:2:1, respectively. The probability of a health hazard (H) caused by these sources is 0.01, 0.005, 0.0005, 0.0001, respectively. Assume, V, I, D, and T are collectively exhaustive and mutually exclusive.
a.) Draw a Venn diagram for this scenario and label it completely
b.) Calculate the probability of a health hazard for the city on a given day
c.) What is the probability of no health hazard in 30 days?
d.) What is the probability of no health hazard in one year (365 days)?