Question

Components 2, 3, and 4 are connected in series, so that their subsystem works only if 2, 3 and 4 all work. The two subsystems are connected in parallel, so the system will work if either subsystem works. The components work independently of one another and the probability that the component works is 0.75 for components 1 and 2 and 0.8 for components 3 and 4. What is the probability that the system works?

Answer 1

0.87

Explanation:

First subsystem now working:

1 - 0.75

0.25

Second subsystem not working:

1 - (0.75 × 0.8 × 0.8)

1 - 0.48

0.52

System wouldn't work if both fail

P(working) = 1 - (0.52×0.25)

1 - 0.13

0.87

Answer 2

0.61

Explanation:

The computation of the probability of the working of the system is shown below:

But before that first we have to find out the total probability of sub-system i.e 2,3 and 4 i.e

`= 0.75*0.8*0.8`

= 0.48

Now the working of the system probability is

= 1 - [(1 - probability of component 1) × (1 - sub system probability)]

= 1 - [(1 - 0.75) × (1 - 0.48)]

= 1 - 0.39

= 0.61

Please find the attachment for better understanding.