How do we find the integer corresponding to this probability problem?












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There are $n$ socks, $3$ of which are red, in a drawer. What is the value of $n$ if, when $2$ of the socks are chosen randomly, the probability that they are both red is $50%$?



MY ATTEMPT



Unfortunately, I am having trouble to model correctly the problem. Could someone help me find the way to solve this exercise? Thanks in advance.



EDIT



This is my try. If we denote by $R$ the event "two red balls have been selected", we get
begin{align*}
mathbb{P}(R) = frac{C(3,2)}{C(n,2)} = frac{6}{n(n-1)} = frac{1}{2} Longleftrightarrow n^{2} - n - 12 = 0 Longleftrightarrow n = 4
end{align*}



I have done this before, but I committed some silly calculation mistakes. Anyway, thanks guys.










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    0












    $begingroup$


    There are $n$ socks, $3$ of which are red, in a drawer. What is the value of $n$ if, when $2$ of the socks are chosen randomly, the probability that they are both red is $50%$?



    MY ATTEMPT



    Unfortunately, I am having trouble to model correctly the problem. Could someone help me find the way to solve this exercise? Thanks in advance.



    EDIT



    This is my try. If we denote by $R$ the event "two red balls have been selected", we get
    begin{align*}
    mathbb{P}(R) = frac{C(3,2)}{C(n,2)} = frac{6}{n(n-1)} = frac{1}{2} Longleftrightarrow n^{2} - n - 12 = 0 Longleftrightarrow n = 4
    end{align*}



    I have done this before, but I committed some silly calculation mistakes. Anyway, thanks guys.










    share|cite|improve this question











    $endgroup$















      0












      0








      0





      $begingroup$


      There are $n$ socks, $3$ of which are red, in a drawer. What is the value of $n$ if, when $2$ of the socks are chosen randomly, the probability that they are both red is $50%$?



      MY ATTEMPT



      Unfortunately, I am having trouble to model correctly the problem. Could someone help me find the way to solve this exercise? Thanks in advance.



      EDIT



      This is my try. If we denote by $R$ the event "two red balls have been selected", we get
      begin{align*}
      mathbb{P}(R) = frac{C(3,2)}{C(n,2)} = frac{6}{n(n-1)} = frac{1}{2} Longleftrightarrow n^{2} - n - 12 = 0 Longleftrightarrow n = 4
      end{align*}



      I have done this before, but I committed some silly calculation mistakes. Anyway, thanks guys.










      share|cite|improve this question











      $endgroup$




      There are $n$ socks, $3$ of which are red, in a drawer. What is the value of $n$ if, when $2$ of the socks are chosen randomly, the probability that they are both red is $50%$?



      MY ATTEMPT



      Unfortunately, I am having trouble to model correctly the problem. Could someone help me find the way to solve this exercise? Thanks in advance.



      EDIT



      This is my try. If we denote by $R$ the event "two red balls have been selected", we get
      begin{align*}
      mathbb{P}(R) = frac{C(3,2)}{C(n,2)} = frac{6}{n(n-1)} = frac{1}{2} Longleftrightarrow n^{2} - n - 12 = 0 Longleftrightarrow n = 4
      end{align*}



      I have done this before, but I committed some silly calculation mistakes. Anyway, thanks guys.







      probability problem-solving






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      edited Jan 8 at 2:58







      user1337

















      asked Jan 8 at 2:45









      user1337user1337

      48210




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          $begingroup$

          Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?






          share|cite|improve this answer









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            $begingroup$

            Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?






            share|cite|improve this answer









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              3












              $begingroup$

              Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?






              share|cite|improve this answer









              $endgroup$
















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                $begingroup$

                Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?






                share|cite|improve this answer









                $endgroup$



                Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Jan 8 at 2:48









                Adam JamilAdam Jamil

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