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Combinations and probability distributions

  1. May 17, 2008 #1
    Can someone please help with the method of how to solve this problem.....

    Question:
    Three balls are thrown at random into 5 bowls so that each ball has the same chance of going into any bowl independently of wherever the other 2 balls fall. Determine the probability distribution of the numberof empty bowls.


    The anwers are below, but i don't understand them. Can it be looked at as a success failure type poblem. with probability of success being that a bowl gets 1 ball: probability = 1/5, and the probability of a failure; 1-1/5 = 4/5. If so how do I use this to obtain the distribution.

    Also can someone please tell me why in this scenario we don't look at the possibility of the ball missing the bowl - because i feel that this should be a possibility in this scenario, which then gives 6 equally likely outcomes, which would mean probabitlity of a success is then 1/6?

    The anwer to this question (which I don't understand) is:
    if we let R = no. of empty bowls

    the distribution of R:
    P(R=2) = 0.48, p(R=3) = 0.48, p(R=4) = 0.04

    Please help!
     
  2. jcsd
  3. May 17, 2008 #2

    tiny-tim

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    Hi SavvyAA3! :smile:
    Yes, that's right! :smile:
    Well, try p(R=4) first … that's the probability that the second and third balls go into the same bowl as the first one … which is … ? :smile:
    erm … REALITY CHECK … ! :rolleyes:

    When you're sitting in the examination room, THE ONLY REALITY IS WHAT'S ON THE QUESTION PAPER … anything else is just a mirage brought about by heat and lack of water and sleep. :wink:
     
  4. May 17, 2008 #3
    why reality check? The question did not state that this is not a possibility - please tell me why I can't assume this?

    Thanks.
     
  5. May 18, 2008 #4
    The question also didn't state that aliens would not grab the balls with a tractor beam or that your dog would not eat them... do you see?
     
  6. May 19, 2008 #5

    tiny-tim

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    Hi montoyas7940! :smile:
    hmm …
    :smile: … is that what happened to you … ? :smile:
     
  7. May 19, 2008 #6
    Hi yourself TT!

    No, fortunately aliens didn't grab my balls. :approve:

    But I read about this guy once...
     
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