A system is composed of five components, each of which is either working or failed. Consider an

experiment that consists of observing the status of each component, and let the outcomes of the ex-

periment be given by all vectors X1, X2, X3, X4, X5), where x¿ is 1 if component i is working and 0 if

component i is not working.

(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, or if components 1, 3, and 5 are all working. Let W be the event that

the system will work. Specify all of the outcomes in W.

(c) Let A be the event that components 4 and 5 have both failed. How many outcomes are in the

event A.

(d) Write out all outcomes in the event An W.