Question

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 (x1, x2, x3, x4, x5), 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?

Answer 1

Answer:  32

Step-by-step explanation:

Given : A system is composed of 5 components, each of which is either working or failed.

We consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector $(x_1, x_2, x_3, x_4, x_5)$

, where $x_i$ is equal to 1 if component i is working and is equal to 0 if component i is failed.

i.e. The total possible outcomes for each component = 2

Now by Fundamental counting principle , the total number of outcomes are in the sample space of this experiment = $2\times2\times2\times2\times2=2^5=32$

[2 outcomes of each component and there area 5 component]

Hence, the number of outcomes in the sample space of this experiment is 32.