A box contains 10 balls, which are 6 W and 4 B. Assume you pick one by one, without replacement

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What is the probability that only $1$ out of the first $4$ you picked are black?



So it is clear that we have picked $4$ balls. Our $4$ spots can be as follows:



$mathrmBWWW$



$mathrmWBWW$



$mathrmWWBW$



$mathrmWWWB$



$4$ ways to orient this.



There are $6$ W balls, from those we must pick $3$.



There are $4$ B balls, from those we must pick $1$.



Thus:



$$fracdisplaystylebinom63binom41displaystylebinom104$$



Is this correct?






probability statistics probability-distributions







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    up vote
    5
    down vote

    favorite
    1












    What is the probability that only $1$ out of the first $4$ you picked are black?



    So it is clear that we have picked $4$ balls. Our $4$ spots can be as follows:



    $mathrmBWWW$



    $mathrmWBWW$



    $mathrmWWBW$



    $mathrmWWWB$



    $4$ ways to orient this.



    There are $6$ W balls, from those we must pick $3$.



    There are $4$ B balls, from those we must pick $1$.



    Thus:



    $$fracdisplaystylebinom63binom41displaystylebinom104$$



    Is this correct?






    probability statistics probability-distributions







    share|cite|improve this question

























      up vote
      5
      down vote

      favorite
      1









      up vote
      5
      down vote

      favorite
      1






      1





      What is the probability that only $1$ out of the first $4$ you picked are black?



      So it is clear that we have picked $4$ balls. Our $4$ spots can be as follows:



      $mathrmBWWW$



      $mathrmWBWW$



      $mathrmWWBW$



      $mathrmWWWB$



      $4$ ways to orient this.



      There are $6$ W balls, from those we must pick $3$.



      There are $4$ B balls, from those we must pick $1$.



      Thus:



      $$fracdisplaystylebinom63binom41displaystylebinom104$$



      Is this correct?






      probability statistics probability-distributions







      share|cite|improve this question















      What is the probability that only $1$ out of the first $4$ you picked are black?



      So it is clear that we have picked $4$ balls. Our $4$ spots can be as follows:



      $mathrmBWWW$



      $mathrmWBWW$



      $mathrmWWBW$



      $mathrmWWWB$



      $4$ ways to orient this.



      There are $6$ W balls, from those we must pick $3$.



      There are $4$ B balls, from those we must pick $1$.



      Thus:



      $$fracdisplaystylebinom63binom41displaystylebinom104$$



      Is this correct?






      probability statistics probability-distributions




      probability statistics probability-distributions






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      edited 2 hours ago









      Isana Yashiro

      1,3031621




      1,3031621










      asked 4 hours ago









      K Split X

      4,006930




      4,006930




















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          Your answer is correct and is a good example of use of the hypergeometric distribution.






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            Your Answer




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            1 Answer
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            up vote
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            Your answer is correct and is a good example of use of the hypergeometric distribution.






            share|cite|improve this answer


























              up vote
              3
              down vote













              Your answer is correct and is a good example of use of the hypergeometric distribution.






              share|cite|improve this answer
























                up vote
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                up vote
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                down vote









                Your answer is correct and is a good example of use of the hypergeometric distribution.






                share|cite|improve this answer














                Your answer is correct and is a good example of use of the hypergeometric distribution.







                share|cite|improve this answer














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                share|cite|improve this answer








                answered 4 hours ago


























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                JMoravitz




























                     

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