A system comprised of three independent components The proba

A system comprised of three independent components. The probability of failure for each component is given.

A1= 0.1 A2= 0.2 A3= 0.3

_________A1________A2________

[ ____________A3______________]

a.)Find the probability the system operates properly

b.)Find the probability that at least two of the components work

c.) Find the probability that the system operates properl if at least one of the components work.

a) prob that the system operates properly

= prob all 3 systems do not fail

= (1-0.1)(1-0.2)(1-0.3)

= 0.9(0.8)(0.7)

= 0.504

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b) Prob atleast 2 of components work = P(A1A2A3\')+P(A1\'A2A3)+P(A1A2\'A3)+P(A1A2A3)

=0.014+0.054+0.024+0.504

= 0.596

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c) Prob for atleast one component working

= 1-Prob for all components fail

= 1-(0.9)(0.8)(0.7)

=1-0.504

=0.496