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I didn't "forget" about it, I contend that case is already handled by GB; "one child is a boy and one child is a girl" is the same as "one child is a girl and o

I didn't "forget" about it, I contend that case is already handled by GB; "one child is a boy and one child is a girl" is the same as "one child is a girl and one child is a boy" and can be expressed as either GB or BG, making GB and BG equivalent.

Tichy 16y ago
No, choosing to not care for order changes the way probabilities have to be calculated. I suppose there was enough discussion about that on this thread already. I guess it is helpful to think about two coin flips instead of boys and girls. Not sure how it is being taught in the US. In Germany we use urn models and learn formulas for drawing balls from urns in different variations. Like returning the balls or not returning the balls, or caring for order or not. All these cases have different formulas attached...
jodrellblank 16y ago
GB and BG take up more area in probability space. If you have a thousand paths in front of you, one leading to a fortune, one to a potion and the rest to a pit of death, you can't say the 998 paths are together equal to the other two just because they all end at the same place. It's much more likely you'll hit the pit of death. It's much more likely to have boy/girl children even though BG and GB look the same at the end. You get as much probability current down each of the wires BG and GB you do down the GG and BB wires, making twice as much in total for BG/GB combined. If there are four buildings, red, green, gray and gray, and you pick one at random you are more likely to end up in a gray building. You dont get to say there are three colours because I can class the two gray buildings as the same the chances are 1/3rd for each colour.
- thwarted 16y ago
  If there are four buildings, red, green, gray and gray, and you pick one at random you are more likely to end up in a gray building. I guess that's where my confusion lies. I see that the chances of picking a grey building the above is 1/2, but I assert that the set of possibilities for the children is "two girls", "different genders" and "two boys". But yours is a good explanation, I see that that "different genders" state has a double chance of occurring compared to the other two states. The Wikipedia article I cited above is interesting in that in one explanation, it bases the different results on interpretation of the givens. I see the problem stated as about a specific man's state, not the chances that a randomly chosen man/family with two children has two boys. In my case, this was a misdirection in trying to understand this.

Tichy 16y ago

No, choosing to not care for order changes the way probabilities have to be calculated. I suppose there was enough discussion about that on this thread already. I guess it is helpful to think about two coin flips instead of boys and girls. Not sure how it is being taught in the US. In Germany we use urn models and learn formulas for drawing balls from urns in different variations. Like returning the balls or not returning the balls, or caring for order or not. All these cases have different formulas attached...

jodrellblank 16y ago

GB and BG take up more area in probability space. If you have a thousand paths in front of you, one leading to a fortune, one to a potion and the rest to a pit of death, you can't say the 998 paths are together equal to the other two just because they all end at the same place. It's much more likely you'll hit the pit of death. It's much more likely to have boy/girl children even though BG and GB look the same at the end. You get as much probability current down each of the wires BG and GB you do down the GG and BB wires, making twice as much in total for BG/GB combined. If there are four buildings, red, green, gray and gray, and you pick one at random you are more likely to end up in a gray building. You dont get to say there are three colours because I can class the two gray buildings as the same the chances are 1/3rd for each colour.

thwarted 16y ago
If there are four buildings, red, green, gray and gray, and you pick one at random you are more likely to end up in a gray building. I guess that's where my confusion lies. I see that the chances of picking a grey building the above is 1/2, but I assert that the set of possibilities for the children is "two girls", "different genders" and "two boys". But yours is a good explanation, I see that that "different genders" state has a double chance of occurring compared to the other two states. The Wikipedia article I cited above is interesting in that in one explanation, it bases the different results on interpretation of the givens. I see the problem stated as about a specific man's state, not the chances that a randomly chosen man/family with two children has two boys. In my case, this was a misdirection in trying to understand this.