In: Statistics and Probability
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? |
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.