A system is composed of four 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...

A system is composed of four 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, x4) 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 2 are both working, or if components 3 and 4
are both working. Specify all the outcomes in the event that the system works.
(c) Let E be the event that components 1 and 3 are both failed. How many outcomes are contained in event
E ?