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Home/ Questions/Consider the system of components connected as in the accompanying picture. Components 1 and 2 are...
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ptntuto
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ptntuto
Asked: April 13, 20222022-04-13T06:45:04+00:00 2022-04-13T06:45:04+00:00In: Statistics-And-Probability

Consider the system of components connected as in the accompanying picture. Components 1 and 2 are…

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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 works). (Round your answer to four decimal places.)

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Independent Events: The probability of either in the events, A and B, which are distinct from each other is not dependent on the event that occurs both. Probability P(AB) is calculated by multiplying the probabilities that are independent of B and A.

 

independent events
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    Poppy Gelbero
    2022-04-13T06:45:07+00:00Added an answer on April 13, 2022 at 6:45 am
    Answer:
    P(system work) = P( Either c1 work or c2 work or both c3 and c4 work)
    = P(c1 ∪ c2 ∪ ( c3∩c4)) = P(c1) + P(c2) + P(c3∩c4) – P(c1∩c2) – P(c1∩c3∩c4) – P(c2∩c3∩c4) + P(c1∩c2∩c3∩c4)
    = P(c1) + P(c2) + P(c3).P(c4) – P(c1).P(c2) – P(c1).P(c3).P(c4) – P(c2).P(c3).P(c4) + P(c1).P(c2).P(c3).P(c4)
    = 0.73 + 0.73 + 0.652 – 0.732 – 0.73 x 0.652 – 0.73 x 0.652 + 0,732 x 0,652
    = 0.95790025
    = 0.9579
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