Question 4613: Hi. The problem is: "Find the probability that two parents with three children have all girls." I have already found out that the answer is 1/8, and how to set the problem up to get that answer, but I just don't understand WHY!! To me, it makes more sense to have it be 1/2 - you have three kids, and each one could be male or female. So, you have three chances/six outcomes. I just don't get why having a boy boy girl, a boy girl boy, or a girl boy boy should be considered as different. Either way, you are having two boys, one girl. Likewise the boy girl girl, girl boy girl, and girl girl boy. You still have the same outcome - one boy, two girls. HELP! If I can't get the logic, I won't be able to sleep : }. Thank you! Maggie
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! The logic here is almost what you wrote, but then you make up some "Maggie logic" :-).
Consider all the possibilities for the 3 kids, with the eldest written first, then the second oldest then the youngest:
BBB
BBG
BGB
BGG
GBB
GBG
GGB
GGG
These are all the possible variations for the 3 children. How many of these outcomes are 3 girls? just 1. Out of how many possible outcomes? 8...answer is therefore 1/8!
Mathematically, we can say:
P(3 girls) = P(first is girl) and P(second is girl) and P(third is girl)
P(3 girls) = 1/2 and 1/2 and 1/2 since for each child the probability of a girl is, yes, 1 out of 2.
But what about the "and". Well, in probability and means multiply, so we get P(3 girls) = 1/2 * 1/2 * 1/2, which again is 1/8.
Hope this helps
jon
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