rudeboyoi
Joined: Mar 28, 2010
• Posts: 2001
January 13th, 2014 at 9:13:16 PM permalink
Quote: Jeepster

Well rudeboyoi as you rounded down your answer I'll have to give it to the Wizard for giving the first correct answer.

Lol I can't do anything right today apparently.
Jeepster
Joined: Jul 7, 2013
• Posts: 84
January 13th, 2014 at 9:23:16 PM permalink
24Bingo, I never said the boy with me was born first.
The only other info I gave you was I had two children.
Therefore you cannot eliminate GB
BG, GB, and BB are all valid and equal possibilities
A photon without any luggage checks into a hotel, he's travelling light.
mwalz9
Joined: Feb 7, 2012
• Posts: 745
January 13th, 2014 at 9:39:55 PM permalink
BG and GB are the same thing!

If I have a dollar and a quarter and you have a quarter and a dollar, we have the same thing!
Jeepster
Joined: Jul 7, 2013
• Posts: 84
January 13th, 2014 at 9:51:59 PM permalink
Quote: mwalz9

BG and GB are the same thing!

Sorry but they are not.
When listing the probabilities the order of occurrence must be factored in.
It may not be intuitive, nevertheless it's important that it's done correctly.

An example, 4 x 2 coin tosses
HH, TT, HT, TH are the 4 possible outcomes
TH and HT are not the same thing, they are separate outcomes
A photon without any luggage checks into a hotel, he's travelling light.
Venthus
Joined: Dec 10, 2012
• Posts: 1125
January 13th, 2014 at 10:16:27 PM permalink
Is HT and TH being different relevant in this question though? We have two unrelated boolean states, with one known state. The question is asking the probability of the unknown state being a specific value, with no value to order. Or, in terms of the original question: There are two kids. One is a boy. What are the odds of the other child being a boy?

With the assumption of a perfect 50/50 ratio, the known state is irrelevant-- there's no bearing on the sex of one child to the other so, for the purposes of the question, that child may as well not exist. What remains is a 50/50 chance of the unknown child being a boy or a girl.

Way I see it, the "trick" to this question is in the wording of "also being a boy", which seems to suggest the odds of BB occurring out of all possible permutations, rather than just out of the combinations where a B already exists. Assuming the two values were known, you'd have BB, BG, GB, GG. BG/GB are functionally identical in this question and can be merged, leaving BB, BG/GB, GG. Of these three, GG can be eliminated as one of the values is confirmed to be B. That leaves BB and BG/GB, or a 50% chance.

Phrasing it in another form:
I just flipped a (perfectly random 2-sided) coin that came up heads. What are the odds of the next flip coming up heads?
Jeepster
Joined: Jul 7, 2013
• Posts: 84
January 13th, 2014 at 10:31:27 PM permalink
Quote: Venthus

I just flipped a (perfectly random 2-sided) coin that came up heads. What are the odds of the next flip coming up heads?

Obviously it's 50/50 for the NEXT flip to be heads
However after the events, if one of your flips was heads and the order was not known, it's only 1 in 3 that the other was also a head. Not 50/50.
If it is known that the first flip was a head then it's 50/50 that the other flip was also a head
A photon without any luggage checks into a hotel, he's travelling light.
Jeepster
Joined: Jul 7, 2013
• Posts: 84
January 13th, 2014 at 10:38:26 PM permalink
As with all these sorts of puzzles the removal of doubt about the answer can be done by running a simulation.
This will prove the answer to be 1 in 3 in the case of the original puzzle.
A photon without any luggage checks into a hotel, he's travelling light.
24Bingo
Joined: Jul 4, 2012
• Posts: 1348
January 13th, 2014 at 11:23:29 PM permalink
Quote: Jeepster

24Bingo, I never said the boy with me was born first.
The only other info I gave you was I had two children.
Therefore you cannot eliminate GB
BG, GB, and BB are all valid and equal possibilities

What's so special about birth order? I'm ordering them "near child, far child," just as I might order two dice "red die, black die." What do I care which die was manufactured first?

I see now what you're getting at:

"I've flipped a fair coin twice, and one of those flips was tails. With that information, what's the probability the other was tails?"

But you've made a mistake by singling out your son as you did in your description of the problem.

Now I've seen you with a son, and there's a child at home whom I know nothing about. A comparable setup would be: "I flipped a fair coin twice, and the more westward-landing one was tails."
The trick to poker is learning not to beat yourself up for your mistakes too much, and certainly not too little, but just the right amount.
Jeepster
Joined: Jul 7, 2013
• Posts: 84
January 13th, 2014 at 11:54:20 PM permalink
Quote: 24Bingo

"I've flipped a fair coin twice, and one of those flips was tails. With that information, what's the probability the other was tails?"

But you've made a mistake by singling out your son as you did in your description of the problem.

Why was it a mistake, it's just a scenario to set out the question.
It gave the info that one child is a boy and the sex of the other is unknown
It did not alter the answer, it's still 1 in 3 that the other is a boy.

I do like your example above though.
A photon without any luggage checks into a hotel, he's travelling light.
michael99000
Joined: Jul 10, 2010
• Posts: 2112
January 14th, 2014 at 12:31:41 AM permalink
Here's why I'm having trouble understanding why the chances the other child is a boy arent 50%.

Let's change the question slightly and say...

You currently have one child and your wife is home pregnant with you're next child. The child I see you with is a boy. What's the chances that the unborn child is also a boy?

According to the question, the world rate for sex of babies is 50/50, so the answer to my question must be the chances that the other unborn child will be a boy is 50%

So, for the question posed by Jeepster, the only difference is the child has already been born. Why does that fact alone make it 17% less likely that the child is a boy. ???

The only difference between the two questions is the physical location of child #2, inside the mother or outside . Seems that shouldn't change the odds it's a boy