
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 2nd, 2018, 07:08 AM  #1 
Newbie Joined: May 2018 From: Germany Posts: 1 Thanks: 0  Find the probability for the event 
May 5th, 2018, 05:15 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
The "complement event" is that there exist at least one empty car and the "PoincareSylvester formula" says that the probability of event A or B (or both) happening is the probability that A happens plus the probability that B happens minus the probability they both happen.

May 5th, 2018, 09:59 AM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,320 Thanks: 1232 
I think the hint in this case leads to a method much harder than necessary. I guess what they are trying to make you do is come up with the probability of the union of $k$ cars being empty $k \in 1,2,\dots N1$ A much much easier approach is to note that in order to maintain at least 1 passenger per car there are $K1$ "slots" between the $K$ passengers that are to be filled with $N1$ "walls". This does assume that passengers are identical which in this problem they essentially are as their probabilities of choosing a car are all identical. So the problem is to determine how many assignments of walls to slots exist and this is simply $n = \dbinom{K1}{N1}$ 

Tags 
event, find, probability 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Probability of a certain event  diselsamm  Advanced Statistics  2  December 17th, 2013 03:09 PM 
Probability of an Event  johnsjg  Probability and Statistics  2  February 1st, 2012 02:08 PM 
Probability of an event  hoyy1kolko  Probability and Statistics  1  April 12th, 2011 09:26 AM 
Probability of an event  hoyy1kolko  Probability and Statistics  1  April 4th, 2011 12:03 PM 
probability of an event  hoyy1kolko  Probability and Statistics  3  April 2nd, 2011 06:42 AM 