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Math Help - theoretical possibilities

  1. #1
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    theoretical possibilities

    I had to use a tree diagram to work out all the possible outcomes (arrangements of boys and girls) in a family of 4 children. I worked out that there are 14 possibilities. From here I am stuck, I have to calculate the theoretical possibility of obtaining 2 girls and 2 boys as a fraction, decimal and percentage. I worked out that there are 6 possibilities out the 14
    bbgg
    ggbb
    bgbg
    gbgb
    gbbg
    bggb

    but where do I go from here??

    Thanks very much in advance!!!
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  2. #2
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    Quote Originally Posted by bookbaby84 View Post
    I had to use a tree diagram to work out all the possible outcomes (arrangements of boys and girls) in a family of 4 children. I worked out that there are 14 possibilities. From here I am stuck, I have to calculate the theoretical possibility of obtaining 2 girls and 2 boys as a fraction, decimal and percentage. I worked out that there are 6 possibilities out the 14
    bbgg
    ggbb
    bgbg
    gbgb
    gbbg
    bggb

    but where do I go from here??

    Thanks very much in advance!!!
    First off, are you sure it's 14 possibilities? I'm counting 16.

    Second, to find the probability of having 2 girls & 2 boys, you divide the number of possibilities of having 2 girls & 2 boys by the total number of possibilities of having 4 children. So it's going to be
    6/16 or 3/8
    .375
    37.5%
    in fraction, decimal, and percentage form, respectively.


    01
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  3. #3
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    Lexington, MA (USA)
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    Hello, bookbaby84!

    yeongil is correct . . . You missed some branches on your tree.


    I had to use a tree diagram to work out all the possible outcomes
    of boys and girls in a family of 4 children.
    I worked out that there are 14 possibilities. . . . . no

    For each of the four children, there are two choices of gender.
    The number of outcomes is: . 2^4 \:=\:16.


    Here they are:

    . . \begin{array}{cccc} 1&2&3&4 \\ \hline \\[-4mm] <br /> <br />
B&B&B&B \\ B&B&B&G \\ \\[-4mm] B&B&G&B \\ B&B&G&G \\  \\[-3mm] B&G&B&B \\ B&G&B&G \\ \\[-4mm] B&G&G&B \\ B&G&G&G  \end{array}

    . . . \begin{array}{cccc}G&B&B&B \\ G&B&B&G \\ \\[-4mm] G&B&G&B \\ G&B&G&G \\ \\[-3mm] G&G&B&B \\ G&G&B&G \\ \\[-4mm]G&G&G&B \\ G&G&G&G \end{array}


    How do we list these cases without omitting any?
    Examine the pattern in the columns.

    In Column-1, the B's and G's change every 8 cases ("half the cases").
    In Column-2, the B's and G's change every 4 cases ("twice as fast").
    In Column-3, the B's and G's change every 2 cases ("twice as fast").
    In Column-4, the B's and G's change every 1 case ("they alternate").

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