A system is subjected to shocks of types 1,2 , and 3 , which are generated by independent homogeneous Poisson processes with respective intensities per hour \(\lambda_{1}=0.2, \lambda_{2}=0.3\), and \(\lambda_{3}=0.4\). A type 1 -shock causes a system failure with probability 1 , a type 2 -shock causes a system failure with probability 0.4 , and shock of type 3 causes a system failure with probability 0.2 . The shocks occur permanently, whether the system is operating or not.

(1) On condition that three shocks arrive in the interval \([0,10 \mathrm{~h}]\), determine the probability that the system does not experience a failure in this interval.

(2) What is the (unconditional) probability that the system fails in \([0,10 \mathrm{~h}]\) due to a shock?