Math Problem Statement
Question content area top Part 1 A circuit system is given in the figure. Assume the components fail independently. The probability that the system works is 0.74886. It is known that the system does not work. What is the probability that the component A also does not work? 0.6 0.7 0.9 0.7 0.9 Question content area bottom Part 1 The probability that the component A also does not work is enter your response here. (Type an integer or decimal rounded to three decimal places as needed.)
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Conditional Probability
Bayes' Theorem
Formulas
P(A \text{ fails} \,|\, \text{System fails}) = \frac{P(\text{System fails} \,|\, A \text{ fails}) \cdot P(A \text{ fails})}{P(\text{System fails})}
P(\text{System Fails}) = 1 - P(\text{System Works})
Theorems
Bayes' Theorem
Suitable Grade Level
College Level or Advanced High School
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