For this question, may i ask why is the inclusion exclusion property required. Why can't I just take P(A can flow to B)= P(A1,A2) + P(A1,A3,A4) since water can flow through from A to B if either 1,2 are open or 1,3,4 are open?

Question 2 The system contains four gates and water flows from A to B. The gates work independently and the probability that a gate is open is p. 1 3 2 4 B (i) What is the probability that water is able to flow from A to B?(i) Let A; = { gate i is open ). P( water flows from A to B - P(Al n [A2 U (A3 n A4)]) = P(A1) P([A2 U (A3 n A4)]) = P(A1) [P(A2) + P(A3 n A4) - P(A2 n A3 n A)] = P(Al) [P(A2) + P(A3) P(A4) - P(A2) P(A3) P(A4)] = p[p + p2 - p3]