Calculate the probability of circuit breakage.A breakage of the electrical circuit occurs if either an element K 1 or both elements K 2 and K 3 break. The elements K 1 , K 2 , K 3 break independently of each other with probabilities respectively 0.3, 0.2, 0.1. Calculate the probability of circuit breakage.

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Calculate the probability of circuit breakage.A breakage of the electrical circuit occurs if either an element       K    1   or both elements       K    2   and       K    3   break. The elements       K    1    ,      K    2    ,      K    3   break independently of each other with probabilities respectively 0.3, 0.2, 0.1. Calculate the probability of circuit breakage.

Julianna Bell · Accepted Answer

Step 1Let Events       A    1    ,      A    2    ,      A    3   denote the failure of       K    1    ,      K    2    ,      K    3   resp.Step 2Probability that system fails  P  (      A    1    ∩            A      ¯        2    ∩            A      ¯        3    )  +  P  (      A    1    ∩      A    2    ∩      A    3    )  +  P  (            A      ¯        1    ∩      A    2    ∩      A    3    )  =  P  (      A    1    ∩            A      ¯        2    ∩            A      ¯        3    )  +  P  (      A    2    ∩      A    3    )  =  (  0.3  )  (  0.8  )  (  0.9  )  +  (  0.2  )  (  0.1  )

A breakage of the electrical circuit occurs if either an element K_1 or both elements K_2 and K_3 break. The elements K_1, K_2, K_3 break independently of each other with probabilities respectively 0.3, 0.2, 0.1. Calculate the probability of circuit breakage.

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