Respuesta :
Answer:
P(F/W)= 0.5/(1-0.5^N)
Step-by-step explanation:
Since each component is independent of the others then the probability that the system works:
P(W) = probability that the system works = 1 - probability that the system do not work
the system will not work only if the N components fail , then
probability that the system do not work= (1-p)^N
where
p= probability that a component works = 0.5
thus
P(W)= 1- (1-p)^N = 1 - 0.5^N
then we can use the theorem of Bayes for conditional probability . Defining the event F= the component 1 works , then
P(F/W)=P(F∩W)/P(W)=P(F)/P(W)= 0.5/(1-0.5^N)
P(F/W)= 0.5/(1-0.5^N)
where
P(F/W)= probability that component 1 works, given that the system is functioning
P(F∩W) = probability that the component 1 works and system functions = P(F) (if the component 1 works , the system will automatically work)
