Math Help - Probability Of Finding The Exact Order Of Children

1. Probability Of Finding The Exact Order Of Children

How would you find the probability of getting the exact order of something? A couple wants to have four children. The only way they want to have those children though is if their first born is a girl and their last child born is a boy, with the gender of the two middle children not mattering. What is the probability of them having a girl first and a boy last happening?

2. Have you tried calculating the number of suitable sequences of four G's and B's as well as the number of all possible such sequences? Each suitable sequence has the form G..B with two elements in the middle.

3. Still Confused

Originally Posted by emakarov
Have you tried calculating the number of suitable sequences of four G's and B's as well as the number of all possible such sequences? Each suitable sequence has the form G..B with two elements in the middle.
No I have not and for this problem order matters so how would you solve it?

No I have not and for this problem order matters so how would you solve it?
I think you misunderstood emakarov hint!

They said fix the first elem as G and the last element as B this gives the string

$G,\_\_\_,\_\_\_,B$

Now remember that G and B are fixed. So how many 4 letter strings can you make that start with G and end with B?

No I have not and for this problem order matters so how would you solve it?
$\begin{array}{*{20}c} B & B & B & B \\ B & B & B & G \\ B & B & G & B \\ B & B & G & G \\ B & G & B & B \\ B & G & B & G \\ B & G & G & B \\ B & G & G & G \\ G & B & B & B \\ G & B & B & G \\ G & B & G & B \\ G & B & G & G \\ G & G & B & B \\ G & G & B & G \\ G & G & G & B \\ G & G & G & G \\ \end{array}$
There are all possible strings.
Now count the favorable cases.

6. Originally Posted by Plato
$\begin{array}{*{20}c} B & B & B & B \\ B & B & B & G \\ B & B & G & B \\ B & B & G & G \\ B & G & B & B \\ B & G & B & G \\ B & G & G & B \\ B & G & G & G \\ G & B & B & B \\ G & B & B & G \\ G & B & G & B \\ G & B & G & G \\ G & G & B & B \\ G & G & B & G \\ G & G & G & B \\ G & G & G & G \\ \end{array}$
There are all possible strings.
Now count the favorable cases.
So would it be 4/16 or .25 or 25% or is there more I need to do?

7. So would it be 4/16 or .25 or 25%
Yes.

8. Originally Posted by emakarov
Yes.
Sweet thanks so much