Probability question please

[Rootz90]

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Given that the probabilities for having a son or a daughter are equal, what is the
probability of having exactly 4 girls out of 6 children

Does order matter in this case? I think it doesn't because you only want 4 girls out of 6 children.
Here is what I came up with

B= boy G= girl

possible arrangements:

BBGGGG
BGBGGG
BGGBGG
BGGGBG
BGGGGB

so each arrangement has a probability of 1/(2)^6? Do I just multiply this number by 5(number of arrangements)?

thanks

 

[two thirty]

Don't know if this is ever covered in DAT prep but I'm in a genetics course now and this was a similar question on my first exam. If you remember Pascals triangle, you could solve it that way.

The binomial equation you'd be dealing with is:

1p^6 + 6p^5q + 15 p^4q^2 + 20p^3q^3 + 15 p^2q^4 + 6pq^5 + 1q^6

p is the probability of boy
q is the probability of girl

Both p and q equals .5 in this situation. So you would use the 15p^2q^4 in this case.

15((.5)^2)((.5)^4)

So yeah, there's probably an easier way, this is just one way I learned from genetics.