Math Help - theoretical possibilities

1. 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??

2. Originally Posted by bookbaby84
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??

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

3. 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]

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").