Suppose that air pollution in a city is caused by the following four sources: automobile exhaust (A), 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 health hazard (H) caused by these sources is 0.01, 0.005, 0.0005, and 0.0001, respectively. 3
Assume A, I, D, and T are collectively exhaustive and mutually exclusive.
Please answer the following questions. Please explain how you solved these as well. I am trying to learn here, not just get an answer.
a) Calculate the probability of a health hazard for the city on a given day?
b) What is the probability of NO health hazard in 30 days?
c) What is the probability of NO health hazard in one year (365 days)?