Bayes Theorem: As an air quality engineer, you Analysis of the airstream mining

Question

Bayes Theorem: As an air quality engineer, you Analysis of the airstream mining specific potlutans in industrial exhaust gas. pollutants: (20 points) 15% 30% 25% 15% 15% Ni Sulfur Oxides (So) (O1) Carbon Monoxide (Co) 05 Ozone For inhalation of NO, the chance of an asthma atta For inhalation of Os, the chance of an asthma attack is Adjacent to this facility, if someone gets a pollutant i For inhalation of PM, the chance of an asthma attack For inhalation of SO, the chance of an asthma a For inhalation of CO, the chance of an asthma atta is 12% is 7% attack is 6% likelihood that the illness was caused by Os? (20 points) induced asthma attack, what is the nduced Extra Credit (4 points) ALL OR NOTHING Your wastewater treatment plant processes sludge to be sent to major processes: a landfill. These are the A: secondary clarifier with a reliability of 0.98 B: gravity thickener with a reliability of 0.95 C: filter press with a reliability of 0.94 D: belt conveyor with a reliability of 0.97 Process A and B must both function for the plant to process sludge. However, D are backu plant to function. p systems to each other. ProcessC and Either one of these processes must work for the entire What is the probability that the entire plant will function as inte nded?

Explanation / Answer

If someone gets a pollution induced Asthma attack, likelihood illness was caused by inhalation of O3 =?

Let A = illness caused by O3 = proportionate to percentage of O3 in air

    B = pollution induced asthma attack

P( A | B) =?

P(A | B) = P( B | A) * P(A) / P(B)

P(B | A) = P( given that caused by O3, prob of asthma attack) = 13%

P(A) = percentage of O3 in air = 15%

P(B) = P(asthm attack irrespective of what causes it) = 12% + 7% + 6% + 13% + 5% = 43%

So, P(A | B) = 0.13 * 0.15 / 0.43 = 0.04534

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