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identical balls are thrown randomly into binsWe throw 2 identical balls randomly into 2 bins. What is the probability that no bin is empty? Assume the bins are distinguishable. |

Re: identical balls are thrown randomly into binsLet'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. |

Re: identical balls are thrown randomly into binsQuote:
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 |

Re: identical balls are thrown randomly into binsI 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. |

Re: identical balls are thrown randomly into binsI 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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