My Math Forum identical balls are thrown randomly into bins

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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
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Re: identical balls are thrown randomly into bins

Quote:
 Originally Posted by greg1313 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.
No, should be 2/4, I think.

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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