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February 19th, 2012, 11:01 AM  #1 
Newbie Joined: Feb 2012 Posts: 2 Thanks: 0  identical balls are thrown randomly into bins
We throw 2 identical balls randomly into 2 bins. What is the probability that no bin is empty? Assume the bins are distinguishable. 
February 20th, 2012, 12:03 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: identical balls are thrown randomly into bins
Let's say you have two identical balls with bin A and bin B. There are three possible outcomes, two balls in bin A, two balls in bin B, or a ball in bin A and a ball in bin B. You have a 1/3 chance that both bins contain a ball, if the probability of landing a ball in either bin is the same. 
February 20th, 2012, 06:53 AM  #3  
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: identical balls are thrown randomly into bins Quote:
1/4 > 2 balls in bin A 1/4 > 2 balls in bin B 2/4 > 1 ball in bin A and 1 ball in bin B  
February 20th, 2012, 08:24 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: identical balls are thrown randomly into bins
I can see 1/2, if there is no chance of missing the bins altogether: it doesn't matter where the first ball lands; the probability that the next ball lands in the other bin is 1/2.

February 20th, 2012, 11:17 PM  #5 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: identical balls are thrown randomly into bins
I agree with the 1/2. In a way it's no different than a typical coin being tossed twice, if you think of the bins as heads and tails. So ball A in bin A and ball B in bin B, or ball A in bin B and ball B in bin A.


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