Scoré: 0.75 of 1 pt 12 of 17 (17 complete) HW score: 89./1 %, 15.25 ot 1 pts &5.

Question

Scoré: 0.75 of 1 pt 12 of 17 (17 complete) HW score: 89./1 %, 15.25 ot 1 pts &5.3.21 Question Help 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 0.15 probability of failure. Complete parts (a) through (c). (a) Would it be unusual to observe one component fail? No Yes Would it be unusual to observe two components fail? No Yes (b) What is the probability that a parallel structure with 2 identical components will succeed? The probability that a parallel structure with 2 identical components will succeed is 0.9775 (Type an integer or a decimal. Do not round.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999? (Round up to the nearest whole number.) Enter your answer in the answer box and then click Check Answer.

Explanation / Answer

C)

probability of failure is for n components =(0.15)n

so probability of success is 1-(0.15)n >0.9999

1-0.9999 >(0.15)n

we can also write it as (0.15)^n <0.0001

taking log both side

n log(0.15)<log(0.0001)

n log(0.15) <-4

n > -4 / log(0.15)

n > 4.8549

n=5

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