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PLEASE EXPLAIN ALL STEPS 4. Suppose the diagram of an electrical system is as given in...
5. Suppose the diagram of an electrical system is as given in the figure below 0.85...
5. Suppose the diagram of an electrical system is as given in the figure below 0.85 0.92 0.95 (a) What is the probability that the system works? Assume the components fail inde- pendently. Round only your final answer to 3 decimals (b) Gien that the system works, what is the probability that the component C is not working? Round only your final answer to 3 decimals
A circuit system is given in the following figure, where the number in each component represents...
A circuit system is given in the following figure, where the number in each component represents the probability that the component works. Assume the components fail independently. (a) What is the probability that the entire system work? (b) Given that the system works, what is the probability that the component A is not working? 0.7 0.7 0.8 0.8 0.8
The probability of A, B, C, and D all equal .98. Please show calculations. 2.3 Conditional...
The probability of A, B, C, and D all equal .98. Please show
calculations.
2.3 Conditional probability and independence Example 3 An electrical system consists of four components as illustrated on the whiteboard. The system works if components A and B work and either of the components C or D works. The reliability (probability of working) of each component is also shown. Find the probability that [a] the entire system works and b] the component C does not work, given...
Question 4 [20 marks] A system consists of five components in two branches as shown in...
Question 4 [20 marks] A system consists of five components in two branches as shown in the following diagram: C-D-E- In other words, the system works if components A and B work or components C, D, and E work. Assume that the components fail independently with the following probabilities: P(A fails) = P(B fails) = 0.1 and P(C fails) = P(D fails) = P(E fails) = 0.2. (a) What is the probability that the system works? (b) Given that the...
4. A parallel system functions whenever at least one of its components works. Suppose you have...
4. A parallel system functions whenever at least one of its components works. Suppose you have two separate parallel systems, A and B, each consisting of n identical components that work independently with probability p. a) Consider parallel system A. Given that the system is functioning, what is conditional probability that component 1 works? (This has nothing to do with B yet.) Suppose system B breaks down (all n of its components fail), but system A remains functional. To get...
Suppose a computer system is assembled out of 100 components, and these are completely assembled before...
Suppose a computer system is assembled out of 100 components, and these are completely assembled before the power is ever applied. Assume that the computer fails to work properly if any component fails a) the rate of defects or each component of the system is only 0 22%, what is the probability that the assembled computer works when switched on, assuming the components are independent? b) For the probability that the system works to be 99% what is the largest...
Problem #7: Suppose that 26% of all steel shafts produced by a certain process are nonconforming...
Problem #7: Suppose that 26% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). (a) In a random sample of 175 shafts, find the approximate probability that between 37 and 53 (inclusive) are nonconforming and can be reworked. (b) In a random sample of 175 shafts, find the approximate probability that at least 49 are nonconforming and can be reworked. Problem #8: A system consists of five components...
5. The figure below shows an electrical circuit in which each of the components located at...
5. The figure below shows an electrical circuit in which each of the components located at points A, B, C, D, and E is independently working or not working. The probability that a component is working is given by the number in the box. .0.8 Let W: where LEA,B,C,D,E) be the event that component L is working, and let T be the event that a signal is transmitted from the input to the output. . LE {A, B, C, D,...
Consider the system of components connected as in the accompanying picture. Components 1 and 2 are...
Consider the system of components connected as in the
accompanying picture. Components 1 and 2 are connected in parallel,
so that subsystem works if and only if either 1 or 2 works; since 3
and 4 are connected in series, that subsystem works if and only if
both 3 and 4 work. If components work independently of one another
and P(component i works) = 0.73 for
i = 1, 2
and = 0.65 for
i = 3, 4,
calculate P(system...
Consider the system of components connected as in the accompanying picture. Components 1 and 2 are...
Consider the system of components connected as in the accompanying picture. Components 1 and 2 are conn or 2 works; since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. If components work independently of one another works)-0.76 for -1,2 and-0.75 for 3,4, calculate Ptsystem works). (Round your answer to four decimal places.,) ected in paralel, so that subsystem works if and only it either 1 and Ptcomponent Need Help?
5. Suppose the diagram of an electrical system is as given in the figure below 0.85 0.92 0.95 (a) What is the probability that the system works? Assume the components fail inde- pendently. Round only your final answer to 3 decimals (b) Gien that the system works, what is the probability that the component C is not working? Round only your final answer to 3 decimals
A circuit system is given in the following figure, where the number in each component represents the probability that the component works. Assume the components fail independently. (a) What is the probability that the entire system work? (b) Given that the system works, what is the probability that the component A is not working? 0.7 0.7 0.8 0.8 0.8
The probability of A, B, C, and D all equal .98. Please show
calculations.
2.3 Conditional probability and independence Example 3 An electrical system consists of four components as illustrated on the whiteboard. The system works if components A and B work and either of the components C or D works. The reliability (probability of working) of each component is also shown. Find the probability that [a] the entire system works and b] the component C does not work, given...
Question 4 [20 marks] A system consists of five components in two branches as shown in the following diagram: C-D-E- In other words, the system works if components A and B work or components C, D, and E work. Assume that the components fail independently with the following probabilities: P(A fails) = P(B fails) = 0.1 and P(C fails) = P(D fails) = P(E fails) = 0.2. (a) What is the probability that the system works? (b) Given that the...
4. A parallel system functions whenever at least one of its components works. Suppose you have two separate parallel systems, A and B, each consisting of n identical components that work independently with probability p. a) Consider parallel system A. Given that the system is functioning, what is conditional probability that component 1 works? (This has nothing to do with B yet.) Suppose system B breaks down (all n of its components fail), but system A remains functional. To get...
Suppose a computer system is assembled out of 100 components, and these are completely assembled before the power is ever applied. Assume that the computer fails to work properly if any component fails a) the rate of defects or each component of the system is only 0 22%, what is the probability that the assembled computer works when switched on, assuming the components are independent? b) For the probability that the system works to be 99% what is the largest...
Problem #7: Suppose that 26% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). (a) In a random sample of 175 shafts, find the approximate probability that between 37 and 53 (inclusive) are nonconforming and can be reworked. (b) In a random sample of 175 shafts, find the approximate probability that at least 49 are nonconforming and can be reworked. Problem #8: A system consists of five components...
5. The figure below shows an electrical circuit in which each of the components located at points A, B, C, D, and E is independently working or not working. The probability that a component is working is given by the number in the box. .0.8 Let W: where LEA,B,C,D,E) be the event that component L is working, and let T be the event that a signal is transmitted from the input to the output. . LE {A, B, C, D,...
Consider the system of components connected as in the
accompanying picture. Components 1 and 2 are connected in parallel,
so that subsystem works if and only if either 1 or 2 works; since 3
and 4 are connected in series, that subsystem works if and only if
both 3 and 4 work. If components work independently of one another
and P(component i works) = 0.73 for
i = 1, 2
and = 0.65 for
i = 3, 4,
calculate P(system...
Consider the system of components connected as in the accompanying picture. Components 1 and 2 are conn or 2 works; since 3 and 4 are connected in series, that subsystem works if and only if both 3 and 4 work. If components work independently of one another works)-0.76 for -1,2 and-0.75 for 3,4, calculate Ptsystem works). (Round your answer to four decimal places.,) ected in paralel, so that subsystem works if and only it either 1 and Ptcomponent Need Help?
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