A system is composed of three 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 (x1, x2, x3),
where xi 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?
b) Suppose that the system will work if components 1 and 3 are both working, or if
component 2 is working. Let W be the event that the system will work. Specify all
the outcomes in W.
c) Let A be the event that components 2 and 3 are both failed. How many outcomes
are contained in the event A?
d) Write out all the outcomes in the event Ac intersects W.