of each other? em has four computers. Computer 1 works with a lity of 0.88; comp

Question

of each other? em has four computers. Computer 1 works with a lity of 0.88; computer 2 works with a probability of 0.78; computer 3 works with a probability of 0.92: computer 4 works with a probability of 0.85. Suppose that the operations of the computers are independent of each other (a) Suppose that the system works only when all four computers are working. What is the probability that the system works? (b) Suppose that the system works only if at least one computer is working. What is the probability that the system works? (c) Suppose that the system works only if at least three computers are working. What is the probability that the system works? 1.6 Posterior Probabilities 1.6.1 Law of Total Probability Let Ai,.... A, be a partition with

Explanation / Answer

a) P(system works) =P(computer 1 works)*P(computer 2 works)*P(computer 3 works)*P(computer 4 works)

=0.88*0.78*0.92*0.85 =0.5368

b)

P(system works) =1-P(none of computer works) =1-(1-0.88)*(1-0.78)*(1-0.92)*(1-0.85)=0.999683

c)

P(system works) =P(3 system works)+P(4 system works)

=P(123 works and not 4+124 works and 3+134 works and not 2+234 works and not 1+1234 works)

=0.88*0.78*0.92*(1-0.85)+0.88*0.78*(1-0.92)*0.85+0.88*(1-0.78)*0.92*0.85 +

+(1-0.88)*0.78*0.92*0.85+0.88*0.78*0.92*0.85 =0.9028

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