If we have three events AiAi with i=1,2,3 with probability 15,14,13 respectively. Let X be the number of these events that occur.
Trying to write down a formula for X in terms of indicators in order to find the expectation of X. Afterwards trying to find Var(X) if each event is disjoint (case 1), each event is independent (case 2), and A1⊆A2⊆A3(case 3).
Any suggestions of how to tackle this problem?