How many outcomes are there in the sample space of this experiment?

Question

A system is composed of 5 components (A, B, C, D, E), each of which is either working or defective. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by {xA, xB, xC, xD, xE} where xi is equal to 1 if the component i is working and is equal to 0 if component i is defective.

a. How many outcomes are there in the sample space of this experiment?

b. Suppose that the system will work if components A, B and C are all working, or if components C, D, and E are all working. Find the probability that the system is working if all outcomes are equally likely.

Answer 1

a) there 2 choices either working or defective for each 5 components

hence the number of outcomes = 2^5 =32

b) since the system will work if components A, B and C are all working, or if components C, D, and E since the outcomes are indepedent

p(system is working if all outcomes are equally likely) = 1/2*1/2*1/2 + 1/2*1/2*1/2 = 1/9 =0.25