A computer has five processing units (PUs). The lifetimes of the PUs are iid Exp( Solution for a exponential distr. P(X p = 0.918 For the computer, P(5 yrs w/o fail) = P(no PU fails) + P(1 PU fails but reconfigures) + P(2 PU fails but reconfigures) + P(3 PU fails but reconfigures) + P(4 PU fails but reconfigures) = (1-p)^5 + 5C1*cp*(1-p)^4 + 5C2*(cp)^2*(1-p)^3 + 5C3*(cp)^3*(1-p)^2 + 5C4*(cp)^4*(1-p) = 0.082^5 + 5*(0.94*0.918)*0.082^4 + 10*(0.94*0.918)^2*0.082^3 + 10*(0.94*0.918)^3*0.082^2 + 5*(0.94*0.918)^4*0.082 =0.2748448 = 0.275 or 27.5% approximately.