Results 1 to 3 of 3

Math Help - Probability: Choosing players from a group.

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    7

    Probability: Choosing players from a group.

    some homework question.

    A total of 6 players is selected at random to form a volleyball team from a group of 10 girls and 5 boys, 6 of the girls and 3 of the boys have played the game before. Find the probability that of the 6 selected
    a) 4 are girls and 2 are boys
    b) at least 4 of the players are girls that have played the game before.
    Last edited by mr fantastic; July 22nd 2010 at 03:33 PM. Reason: Re-titled.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Quote Originally Posted by phillychum View Post
    some homework question.

    A total of 6 players is selected at random to form a volleyball team from a group of 10 girls and 5 boys, 6 of the girls and 3 of the boys have played the game before. Find the probability that of the 6 selected
    a) 4 are girls and 2 are boys
    b) at least 4 of the players are girls that have played the game before.
    For (a) Calculate (10C4 x 5C2)/15C6

    (b) sorry, i misinterpreted this as among the 6 selected players who are experienced, at least 4 of the players are girls that have played the game before. Thanks Soroban.
    Last edited by mathaddict; July 22nd 2010 at 06:45 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645
    Hello, phillychum!

    There are 10 girls and 5 boys who play volleyball.
    A team of 6 players are selected at random
    6 of the girls and 3 of the boys have played the game before.

    Some players are Experienced, others are New to the game.

    . . \begin{array}{c||c|c||c|}<br />
& \text{Exp} & \text{New} & \text{Total} \\ \hline \hline<br />
\text{Girls} & 6 & 4 & 10 \\ \hline<br />
\text{Boys} & 3 & 2 & 5 \\ \hline \hline<br />
\text{Total} & 9 & 6 & 15 \\ \hline<br />
\end{array}




    Find the probability that of the 6 selected

    a) 4 are girls and 2 are boys

    There are: . {15\choose6} possible teams.

    4 girls, 2 boys: . {10\choose4}{5\choose2} teams.


    Therefore: . P(\text{4G 2B}) \:=\:\dfrac{{10\choose4}{5\choose2}}{{15\choose6}} \:=\:\dfrac{2100}{5005} \:=\:\dfrac{60}{143}




    b) at least 4 of the players are girls that have played the game before.

    There are 6 Experienced girls (G^*) and 9 Others.


    There are three cases to consider:

    . . \begin{array}{cccccc}(1) & 4\;G^*,\:2\text{ Others:} & {6\choose4}{9\choose2} &=&  540 \\ \\[-3mm]<br />
(2) & 5\:G^*,\:1\text{ Other:} & {6\choose5}{9\choose1} &=& 54 \\ \\[-3mm]<br />
(3) & 6\;G^*,\:0\text{ Other:} & {6\choose6}{9\choose0} &=& 1 \\ \\[-4mm] \cline{3-5}<br />
& & \text{Total:} & & 595  \end{array}


    Therefore: . P(\text{at least 4 }G^*) \;=\;\dfrac{595}{5005} \;=\;\dfrac{17}{143}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. probability of choosing two word
    Posted in the Statistics Forum
    Replies: 3
    Last Post: October 5th 2010, 06:43 AM
  2. Probability of choosing workers
    Posted in the Statistics Forum
    Replies: 1
    Last Post: February 10th 2010, 06:16 PM
  3. its anther probability of choosing ball question
    Posted in the Statistics Forum
    Replies: 2
    Last Post: May 26th 2009, 03:45 AM
  4. Probability of choosing balls in an urn.
    Posted in the Statistics Forum
    Replies: 1
    Last Post: May 3rd 2008, 05:50 AM
  5. Probability of choosing the same number?
    Posted in the Statistics Forum
    Replies: 4
    Last Post: October 7th 2007, 12:51 AM

Search Tags


/mathhelpforum @mathhelpforum