A certain computer system consists of two basic components: (a) the CPU, and (b)

Question

A certain computer system consists of two basic components: (a) the CPU, and (b) the monitor. In order for the system as a whole to be functioning, BOTH components have to be working. The probability at any one time that the CPU is working is 90%, and the probability for the monitor is 70%. What's the total "reliability" of the system -- that is, the probability that the system as a whole will be functioning? Assume first of all that whether the monitor is working is not independent of whether the CPU is working.

Assume now that whether the monitor is working IS independent of whether the CPU is working. What now is the probability that the system as a whole is functioning (this probability is called the computer system's overall "reliability")?

Select one:

cannot be determined without further information

160%

63%

27%

97%

Continuing, suppose now that there is a "back-up" monitor that we can use if our regular monitor isn't working. The back-up monitor has the same reliability as the primary one (70%), but we assume that whether one is working is independent of whether the other one is working. What's the probability that at least one of the two monitors will be working?

Select one:

49%

140%

91%

51%

9%

Still assuming that all these components are "independent", what's the reliability of the system as a whole, with the backup monitor included?

Select one:

79.9%

81.9%

44.1%

86.3%

99.1%

Explanation / Answer

(a) Let

R denote the reliability.

R(CPU) = 0.90

R(Monitor) = 0.70.

So, R(Computer) = R(CPU) X R(Monitor) = 0.90 X 0.70 = 0.63

So, the correct option is:

63%

(b) Probability of one monitor working = 0.70.

Probability of one monitor not working = 1 - 0.70 = 0.30.

Probability of at least any one of 2 monitors working :

= 1 - Probability both monitors not working = 1 - 0.30 X 0.30 = 1 - 0.09 = 0.91

So, the correct option is:

91%.

(c) Reliability of the system = P(CPU) X P(Monitor)

                                             = 0.90 X 0.91 = 0.819.

So, the correct option is:

81.9%

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