Consider a system that consists of n independent components C1,C2,…,Cn. Let Ei be the event that component Ci functions satisfactorily during a mission of specified length.
a. (i) State clearly what it means for the events E1,E2,…,En to be independent.
b. (ii) If the system works only when all the n components work, derive an expression for the probability that the system works in terms of P(Ei),i=1,2,…,n.
c. (iii) If the system works provided at least one of the n components works, derive an expression for the probability that the system works in terms of P(Ei),i=1,2,…,n. Show each logical step clearly.