Dondarrion wrote:
donkadsw wrote:
Why are we ordering here? I mean, I would think BBGG to be the same as BGBG - since the question asks about exactly 2 girls and 2 boys, irrespective of any order of delivery.
We have 5 possibilities: 4 boys, 3 boys and 1 girl, 2 boys and 2 girls, 1 boy and 3 girls, and finally all 4 girls.
So shouldn't the probability be 1/5? too simplistic - I know. but where am I wrong?
Bump seeking an answer to the question above:
I got 1/5 as well.
BBBB
BBBG
BBGG
GGGB
GGGG
1/5 outcomes
The question doesn't say anything about the order. How do we know when order matters?
In this case we are saying that the probability of BGGG is the same as the probability of BBGG. But that is not so.
You can have 1 boy and 3 girls in 4 ways: BGGG, GBGG, GGBG, GGGB
But you can have 2 boys and 2 girls in 6 ways: BBGG, BGGB, GGBB, BGBG, GBGB, GBBG
So the probability depends on the number of ways in which you can get 2 boys and 2 girls.
Think of it this way: if you throw two dice, is the probability of getting a sum of 2 same as the probability of getting a sum of 8? No.
For sum fo 2, you must get 1 + 1 only.
For sum of 8, you could get 4 + 4 or 3 + 5 or 2 + 6 etc.
So probability of getting sum of 8 would be higher.
In the same way, the order matters in this question.