A system is composed of 4 components, each of which is either working or failed.

Question

A system is composed of 4 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 (x_1, x_2, x_3, x_4), where x_i is equal to one if component i is working and is equal to 0 if component i is failed. How many outcomes are in the sample space of this experiment? 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 4 are all working. Let W be the event that the system will work. Specify all the outcomes in W

Explanation / Answer

1) A) AS THERE Are 2 choice for each vector (x1,x2,x3,x4)

hence total outcomes =24 =16

b)as outcome of vector is represented by 1 when it is working and 0 when it is not working, hence

when 1 and 2 are working outcomes={1100,1101,1110,1111} ,

when 3 and 4 are working outcomes ={0011,0111,1011,1111}

when 1,3,4 are working outcome ={1011,1111}

hence total number of outcomes in W ={0011,0111,1011,1100,1101,1110,1111}

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