stions correctly?
6. A complex electronic system is built with a certain number of backup components in its
subsystems. One subsystem has four identical components, each with a probability of .2 of failing
in less than 1000 hours. The subsystem will operate if any two of the four components are
operating. Assume that the components operate independently. Find the probability that;
(a) Exactly two of the four components last longer than 1000 hours
(B) The system operates longer than 1000 hours
The probability of failing in less than 1000 hours=0.2
This implies that the probability of lasting longer than 1000 hours is 0.8.
a) Exactly two of the four components last longer than 1000 hours
"P(X=x)={n\\choose x}*p^x*q^{n-x}"
"P(X=2)={4\\choose 2}*0.8^2*0.4^2"
=0.1536
b) The system operates longer than 1000 hours
"P(X\\geq 2)=\\sum_2^4 {4\\choose x}*0.8^x*0.2^{4-x}"
=0.9728
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