probability

Question

9 passengers take a train with 3 sleeping cars. Each passenger chooses the car randomly.
What is the probability that
a) all passengers choose the first car;
b) all passengers choose the same car;
c) at least one passenger chooses the first car;
d) each car is chosen by three passengers?

Answer 1

 

Assuming independence of passenger selection,

and taking the naive approach:

 

(A)

 

     (1/3)^9 = 0.0000508052634291

 

(B)  (1/3)^8 = 0.0001524158

 

(C) is the same as 1 minus all passengers choose cars 2 or 3

 

       1 - (2/3)^9 = .974

 

(d) 3*(1/3)^3 = 3/27 = 1/9 = 0.1