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

Mbalisikerc

Answered question

2022-07-20

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.

Answer & Explanation

Julianna Bell

Julianna Bell

Beginner2022-07-21Added 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 )

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?