Another kid probability one…

[RT898]

Help me settle a family argument. What is the likelihood of 3 brothers each having 2B2G of their 4 kid family?

My proposed answer:

5.3% chance

3/8^3

6/16=3/8
BBBB, BBBG, BBGB, BBGG(1)
BGBB, BGBG(2), BGGB(3), BGGG
GGGG, GGGB, GGBG, GGBB(4)
GBGG, GBGB(5), GBBG(6), GBBB

 

[BigBeachBanana]

Assuming each birth is independent of the others, and the birth of boys and girls is equally likely.
Each brother has a probability of [math]{4 \choose 2}(.5)^2(.5)^2=.375[/math]Then, the probability of 3 brothers is [imath].375^3\approx 5.3\%[/imath]