Answer to Question #185309 in Statistics and Probability for Mariam

Question

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

Answer 1

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