A parallel system functions whenever at least one of its components works. Consider a parallel system of n components, and suppose that each component works independently with probability 1/2 . Find the conditional probability that component 1 works given that the system is functioning.
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- Consider a system that functions whenever at least five of its seven components work. Suppose that each component works independently with probability 1/4. Find the probability that the system will function. Find the probability that only five components work given that the system is functioning. Find the probability that Component 3 works given that the system is functioning.For a parallel structure of identical components, the system can succeed if at least one of the components succeeds, Assume that components fail independently of each other and that each component has a 0.08 probability of failure. Complete parts (a) through (c) below. (a) Would it be unusual to observe one component fail? Two components? It V be unusual to observe one component fail, since the probability that one component fails,, is V than 0.05. It V be unusual to observe two components fail, since the probability that two components fail,. is v than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.) P Type here to search lypFor a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.09 probability of failure. Complete parts (a) through (c) below. (a) Would it be unusual to observe one component fail? Two components? It V be unusual to observe one component fail, since the probability that one component fails, |, is V than 0.05. It V be unusual to observe two components fail, since the probability that two components fail, is V than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.)
- A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is 0.9, the probability that at least one of the two components does so is 0.92, and the probability that both components do so is 0.85. Given that the first component functions in a satisfactory manner throughout its design life, what is the probability that the second one does also?For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.09 probability of failure. Complete parts (a) through (c) below. T.... (a) Would it be unusual to observe one component fail? Two components? be unusual to observe one component fail, since the probability that one component fails, than 0.05. It be unusual to observe two components fail, since the probability that two components fail,, is than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.) O Time Remaining: 02:29:14 Next Left RahtA system contains two components, A and B. The system will function only if both components function. The probability that A functions is 0.98, the probability that B functions is 0.95, and the probability that either A or B functions is 0.99. What is the probability that the system functions?
- For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.21 probability of failure. How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999?For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.22 probability of failure. Complete parts (a) through (c) below. ..... (a) Would it be unusual to observe one component fail? Two components? It be unusual to observe one component fail, since the probability that one component fails,, is than 0.05. It be unusual to observe two components fail, since the probability that two components fail, , is than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999? (Type a whole number.) DEC 16 étv J 280 MacBook Air 80 DII F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 公8For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.09 probability of failure, Complete parts (a) through (c) below. ..... (a) Would it be unusual to observe one component fail? Two components? be unusual to observe one component fail, since the probability that one component fails, is than 0.05. It be unusual to observe two components fail, since the probability that two components fail, than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succe is greater than 0.9998? (Type a whole number.) 02 C4 888 Left Rahi S B. Control CommaRnd uondo uond
- For a parallel structure of identical components, the system can succeed if at least one of the components succeeds. Assume that components fail independently of each other and that each component has a 0.08 probability of failure. Complete parts (a) through (c) below. ..... (a) Would it be unusual to observe one component fail? Two components? It be unusual to observe one component fail, since the probability that one component fails, is than 0.05. It be unusual to observe two components fail, since the probability that two components fail, is than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.) Time Remaining: 02:38:20 Next MacBook Pro 888 OOD F7 FB F10 F5 F6 F4 24 3 4 6 eft ERConsider the system below, and assume that each component functions independently of the others with probability p = 0.8. What is the probability that the entire system works?A system consists of two components. The probability that the second component functions in a satisfactorymanner during its design life is 0.9, the probability that at least one of the two components does so is 0.96,and the probability that both components do so is 0.75. Given that the first component functions ina satisfactory manner throughout its design life, what is the probability that the second one does also?
