A system is composed of 5 components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector:
(x_1, x_2, x_3, x_4, x_5)
where x_i (note, the subscript is the letter " i ", not 1)
is equal to 1 if component i is working, and is equal to 0 if component i is failed.
(a). How many outcomes are in the sample space of this experiment? Give an explanation, not just an answer.
(b) Suppose that the system will work if components 1 and 2 are both working, or if components 3 and 4 are both working, or if components 1,3, and 5 are all working. Let W be the event that the system will work. Specify all the outcomes in W. Again, give an explanation to support your answer.
This solution is comprised of a detailed explanation to answer how many outcomes are in the sample space of this experiment.