Genetics Class - Question 3.21

[ebayandres]

Im taking a genetics class... i was able to figure out the answer but my answer does not match the answer on back of the book. Please help.

 

heres the question:

 

3.21) In a family of six children, what is the chance that at lease 3 are girls?

[Mr Skeptic]

So what's your answer and how did you arrive at it?

[ebayandres]

What I got was... Sex is a 50 / 50 shot. So, If they want at least three girls, I did:

 

Kid one girl : 1/2

Kid two girl : 1/2

Kid three girl : 1/2

 

1/2 x 1/2 x 1/2 is 1/8th... but the book says..

 

Book Answer :

(20/64)+(15/64)+(6/64)+(1/64)=42/64

[Mr Skeptic]

That would be the probability of having 3 girls, not at least 3 girls out of 6 children. To get 3 girls out of 6 children, you need 3 boys and 3 girls. But, the problem does not say they have to be in any particular order, so every possible way they can be arranged counts as well. But, there could also be 4 girls and 2 boys, or 5 girls and 1 boy, or 6 girls and no boys.

 

In any case, as you said, there is 1/2 chance for each, so (1/2)^6 = 1/64, hence that term. To see how many possible ways to arrange them, you could find each combination yourself, or use the choose function (binomial coefficient). I recommend the latter as your teacher is likely to hit you with a big one, and you don't want to be counting 1000 combinations on a test.

Edited October 7, 2009 by Mr Skeptic
misread problem