Probability Genetics question
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Probability Genetics question
Hello all,
So I know probability is a pretty easy endeavor, but the wording of this question has me a little confused as to how to go about structuring me equation and response.
Question: What percentage of families with four children can we expect to have two boys and two girls?
I know its a 50% chance of each (for the purposes of this problem). I am asked to use binomial expansion to solve.
I underlined the percentage of families because that is where it differs from all the other problems I've encountered thus far.
I don't know whether to include just the odds of the different combinations of children a couple may potentially have
bbgg
bbbg
gggb
bbbb
gggg
...or whether to structure it such that I am considering the order in which they're having them also, and how that affects the probability.
It's been years since I've done binomial distribution and this is a distanceed class, I'm not even sure how to go about structuring it. Any help would be greatly appreciated.
Thank you!
So I know probability is a pretty easy endeavor, but the wording of this question has me a little confused as to how to go about structuring me equation and response.
Question: What percentage of families with four children can we expect to have two boys and two girls?
I know its a 50% chance of each (for the purposes of this problem). I am asked to use binomial expansion to solve.
I underlined the percentage of families because that is where it differs from all the other problems I've encountered thus far.
I don't know whether to include just the odds of the different combinations of children a couple may potentially have
bbgg
bbbg
gggb
bbbb
gggg
...or whether to structure it such that I am considering the order in which they're having them also, and how that affects the probability.
It's been years since I've done binomial distribution and this is a distanceed class, I'm not even sure how to go about structuring it. Any help would be greatly appreciated.
Thank you!
The probability for gggg is (1/2)^4 = 1/16 = 6.25 %
The same for bbbb. But for others, it changes:
For example for 1 g and 3 b its:
gbbb: 6.25 %
bgbb: 6.25 %
bbgb: 6.25 %
bbbg: 6.25 %
Total: 25 %
As using binomial expansion it's:
(g+b)^4 = g^4 + 4(g^3)b + 6(g^2)(b^2) + 4g(b^3) + b^4
2 boys and 2 girls = 6(g^2)(b^2) = 6 x 1/4 x 1/4 = 0.375 which is 37.5%
So, the question is why I choose this way instead of saying 20%. I think the order is important. Because, each subsets of a combination is a different event. Thus, we should use permutation instead of combination.
In other words, if someone says 'families that have 2 boys and 2 girls', we consider every familiy with this condition (ggbb, gbbg etc.).
The same for bbbb. But for others, it changes:
For example for 1 g and 3 b its:
gbbb: 6.25 %
bgbb: 6.25 %
bbgb: 6.25 %
bbbg: 6.25 %
Total: 25 %
As using binomial expansion it's:
(g+b)^4 = g^4 + 4(g^3)b + 6(g^2)(b^2) + 4g(b^3) + b^4
2 boys and 2 girls = 6(g^2)(b^2) = 6 x 1/4 x 1/4 = 0.375 which is 37.5%
So, the question is why I choose this way instead of saying 20%. I think the order is important. Because, each subsets of a combination is a different event. Thus, we should use permutation instead of combination.
In other words, if someone says 'families that have 2 boys and 2 girls', we consider every familiy with this condition (ggbb, gbbg etc.).
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