(2) A chemical plant produces a variate of products using four different processes, the available labor is sufficient only to run one process a time. The plant manager knows that the discharge of dangerous pollution into the plant waste water system and thence into a nearby stream is dependent on which process equipment is in operation. The probability that a particular process will be producing dangerous pollution is as shown below: Process A 40% Process B 5% Process C 30% Process D 10% All other processes in the plant are considered harmless. In a typical month the relative likelihoods of process A, B, C, and D operating through the month are 2:4:3:1, respectively. (a) What is the probability that there will be no dangerous pollution discharged in a given month? (b) If dangerous pollution is detected in the plant discharge, what is the probability that process A was operating? (c) The pollution products that are discharged by the various processes have different probability of producing fish kill in the stream, as follows Process Probability of fish kill A 0.9 B 0.1 C 0.8 0.3 Based on these assumptions, that is the probability that fish will be killed by pollution in the stream in a given month?
(2) A chemical plant produces a variate of products using four different processes, the available labor is sufficient only to run one process a time. The plant manager knows that the discharge of dangerous pollution into the plant waste water system and thence into a nearby stream is dependent on which process equipment is in operation. The probability that a particular process will be producing dangerous pollution is as shown below: Process A 40% Process B 5% Process C 30% Process D 10% All other processes in the plant are considered harmless. In a typical month the relative likelihoods of process A, B, C, and D operating through the month are 2:4:3:1, respectively. (a) What is the probability that there will be no dangerous pollution discharged in a given month? (b) If dangerous pollution is detected in the plant discharge, what is the probability that process A was operating? (c) The pollution products that are discharged by the various processes have different probability of producing fish kill in the stream, as follows Process Probability of fish kill A 0.9 B 0.1 C 0.8 0.3 Based on these assumptions, that is the probability that fish will be killed by pollution in the stream in a given month?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:(2) A chemical plant produces a variate of products using four different processes, the available labor is
sufficient only to run one process a time. The plant manager knows that the discharge of dangerous
pollution into the plant waste water system and thence into a nearby stream is dependent on which
process equipment is in operation. The probability that a particular process will be producing dangerous
pollution is as shown below:
Process A 40%
Process B 5%
Process C 30%
Process D 10%
All other processes in the plant are considered harmless.
In a typical month the relative likelihoods of process A, B, C, and D operating through the month are
2:4:3:1, respectively.
(a) What is the probability that there will be no dangerous pollution discharged in a given month?
(b) If dangerous pollution is detected in the plant discharge, what is the probability that process A was
operating?
(c) The pollution products that are discharged by the various processes have different probability of
producing fish kill in the stream, as follows
Process
Probability of fish kill
A
0.9
В
0.1
C
0.8
0.3
Based on these assumptions, that is the probability that fish will be killed by pollution in the stream in a
given month?
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