A parallel system functions whenever at least one of its components works. Consider a parallel system of 5 components, and suppose that each component works independently with probability 0.4. Given that the system is functioning, what is the probability that component 4 works?

Probability that component 4 works given that the system is functioning = 0.434 .

Step-by-step explanation:

We are given that a parallel system functions whenever at least one of its components works.

There are parallel system of 5 components and each component works independently with probability 0.4 .

Let A = Probability of component 4 working properly, P(A) = 0.4 .

Also let S = Probability that system is functioning for whole 5 components, P(S)

Now, the conditional probability that component 4 works given that the system is functioning is given by P(A/S) ;

P(A/S) =  {Means P(component 4 working and system also working)

divided by P(system is functioning)}

  P(A/S) =  {In numerator it is P(component 4 working) and in

                denominator it is P(system working) = 1 - P(system is not working)}

Since we know that P(system not working) means that none of the components is working in system and it is given with the probability of 0.6 and since there are total of 5 components so P(system working) = 1 - .

 Hence, P(A/S) = = 0.434.    

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

i would need to see the dot plot : )