The reason is that we are simply dealing with the unconditional probability that . It is true that the probability changes when people get off; but then we would be talking about the probability that given that j passengers had gotten off, or something like that.
It is true that . That is just another way of saying that the 's are not independent. But the solution I gave does not require their independence.
I say again: even if and are not independent. It's hard to swallow, I know.