A train has got five train cars, each one with N seats. There are 150 passengers who randomly choose one of the cars. What is the probability that everyone will get a seat?
I think that what is asking me is "what is the probability that each wagon is chosen by no more than N passengers"?
Given a wagon, the probability of having $n<N$ people in it is given by $$p_N=\sum\limits_{n=0}^N \binom{150}{n}0.2^n 0.8^{150-n}$$.
I thought of the answer being $p_N^5$.. but I think that the events
- wagon a is chosen by no more than N passengers
- wagon b is chosen by no more than N passengers
- wagon c is chosen by no more than N passengers
- wagon d is chosen by no more than N passengers
- wagon e is chosen by no more than N passengers
are far from being independent... So what could I do? Thanks a lot