We have a system that has 2 independent components. Both components must function in order for...

We have a system that has 2 independent components. Both components must function in order for the system to function. The first component has 9 independent elements that each work with probability 0.91. If at least 6 of the elements are working then the first component will function. The second component has 4 independent elements that work with probability 0.86. If at least 2 of the elements are working then the second component will function.

(a)	[3 marks] What is the probability that the system functions?

(b)	[2 marks] Suppose the system is not functioning. Given that information, what is the probability that the second component is not functioning?

Solutions

Expert Solution

a) First we compute here the probability that each of the two independent components function:

P( Component 1 functions) = Probability that at least 6 of the 9 independent elements work

Similarly for the second component we have the probability as:

Now probability that the system works is computed here as:
= P(component 1 works)P(component 2 works)

= 0.9943*0.9902

= 0.9846

Therefore 0.9846 is the required probability here.

b) Given that the system is not functioning, probability that the second component is not functioning is computed here as:

= Probability that the second component is not functioning / Probability that the system is not functioning

= (1 - 0.9902) / (1 - 0.9846)

= 0.6345

Therefore 0.6345 is the required probability here.

orchestra answered 1 year ago

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