The components operate independently, so the probability of "total" system failure is the same as the product of each probability of component failure. That is, if [tex]A_i[/tex] denotes the event that component [tex]i[/tex] fails, then
[tex]\mathbb P(A)=\mathbb P(A_1\cup\cdots\cup A_6)=\mathbb P(A_1)\times\cdots\times\mathbb P(A_6)[/tex]
The [tex]A_i[/tex] are independent and identically distributed, so [tex]\mathbb P(A_i)=\mathbb P(A_j)[/tex] for all [tex]i,j[/tex]. So
[tex]\mathbb P(A)=\mathbb P(A_1)^6=0.02^6=6.4\times10^{-11}=0.000000000064[/tex]
