An appliance consists of three elements of type A, three of type B, four of type C. The appliance stops working if less than two elements of a kind are functional. In some interval of time $t$, the probability of failure of the components is:
$P(A)=0.1, P(B)=0.1, P(C)=0.2$
-What is the probability of the appliance failing in time $t$?
-Given that the appliance failed, what is the probability of the failure being a result of type A or C failing?
I'm not sure how to set up the calculations for this. I tried doing the first one with the law of total probability, (either the failure was caused by A, B or C - type), but these are not independent. Would appreciate hints on how to begin.