Question 1022279: A Machine Has Three Components Even If One Component Fails Machine Will Not Work Failure Rate Of Component A Is 0.08 Component B Is 0.06 And C Is 0.09 What Is Probability That Machine Will Fail and failure occurrence of three components are independent
Answer by mathmate(429)   (Show Source):
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Question:
A Machine Has Three Components Even If One Component Fails Machine Will Not Work Failure Rate Of Component A Is 0.08 Component B Is 0.06 And C Is 0.09 What Is Probability That Machine Will Fail and failure occurrence of three components are independent
Solution:
This is a situation similar to a three-step experiment.
We want to find the probability where each of the three steps is a success.
The success probabilities are the complement of the failure rates, namely
(1-0.08),(-0.06) and (1-0.09), or {0.92, 0.94, 0.91).
Thus the probability of all three are success is the product of the probabilities,
P(success)=0.92*0.94*0.91=0.786968.
The probability of any one failing is the complement of success,
P(failure) = 1-0.786968 = 0.2130
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