AND Gate
If A1, A2, ..., An are the inputs and A is the output of an AND gate, then the probability of (occurrence of the output of) the gate is:
Pr{A} =Pr{A1}Pr{A2\A1}.....Pr{An\A1,A2....,An-1}
If all events are independent, then:
Pr{A} =Pr{A1}Pr{A2}.....Pr{An}
Example
Events A and B are independent and are connected to an AND gates. Given that the probabilities of these events are 0.1 and 0.2 respectively, then the gate probability is:
(0.1)(0.2)=0.002