The probability of exceeding the ozone air quality standard in two cities A and

Question

The probability of exceeding the ozone air quality standard in two cities A and B are 0.12 and 0.07, respectively. However, should the ozone standard be exceeded in city A, the likelihood of exceeding the standard in city B would increase to 0.48.

a. What is the probability that the ozone levels in both cities exceed the standard?

b. What is the probability that ozone levels in at least one of the two cities exceed the standard?

c. Should the ozone standard be exceeded in at least one of the cities, what is the probability that the ozone standards will be exceeded in both cities?

Please show your work!

Explanation / Answer

a)P(A) =0.12 and P(B) =0.07

as well P(B|A) =0.48

a) probability that the ozone levels in both cities exceed the standard=P(A n B) =P(A)*P(B|A) =0.12*0.48=0.0576

b)  probability that ozone levels in at least one of the two cities exceed the standard

=P(A U B) =P(A)+P(B)-P(A n B) =0.12+0.07-0.0576=0.1324

c)  probability that the ozone standards will be exceeded in both cities given exceeded in at least one of the cities

=P(A n B|A U B) =P(A n B)/P(A U B) =0.0576/0.1324=0.4350

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