I'm going to disagree with you; I still think that

.

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.