Chapter 2, Problem 2.5P

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 $\left(x_1,x_2,x_3,x_4,x_{25}\right)$, where $x_i$ 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, or if components 1, 3, and 5 are all working. Let it be the event that the system will work. Specify all the outcomes in IV.

c. Let A be the event that components 4 and 5 are both failed. How many outcomes are contained in the event A?

d. Write out all the outcomes in the event AW.