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.

Mbalisikerc 2022-07-20 Answered
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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Answers (1)

Julianna Bell
Answered 2022-07-21 Author has 19 answers
Step 1
Let Events A 1 , A 2 , A 3 denote the failure of K 1 , K 2 , K 3 resp.
Step 2
Probability 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 )
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