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February 19th, 2012, 11:01 AM   #1
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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.
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February 20th, 2012, 12:03 AM   #2
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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.
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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
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February 20th, 2012, 08:24 AM   #4
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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.
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February 20th, 2012, 11:17 PM   #5
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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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