1) A building has 10 floors above the basement. If 12 people get into an elevator at the basement, and each chooses a floor at random to get out, independently of the others, at how many floors do you expect the elevator to make a stop to let out one or more of these 12 people?
2) Let A1, A2, and A3 be events with probabilities 1/5, 1/4, and 1/3, respectively. Let N be the number of these events that occur.
a) Write down a formula for N in terms of indicators.
b) Find E(N)
In each of the following cases, calculate Var(N):
c) A1, A2, A3 are disjoint;
d)they are independent;
e) A1 is a subset of A2 is subset of A3.
I'm having a hard time figuring these out. Id really appreciacte any help!