Probability Puzzle

[magnemoe]

6 minutes ago, YNM said:

 

yes and we could define pi as 6.283 if we wanted, this would require removing the 2* in formulas with it. 
again its an definition who is precise as long as you follow the rules. 

And for the 1/0=0 argument this is for computers not math there it as OP is undefined, in computer terms this is an NaN or not an number.
Say you try to convert an input field into an number and its value is "a" who is not an number. This you has to trap and handle, either by giving an error to user or simply setting it to 0 in cases you don't bother with an error message. 

on the other hand then dividing on zero you tend to want an 0 out in pretty much all cases so it would be easier and generate fewer crashes if you default returned 0 and you had to trap for x being 0 in z=y/x rather than z=0; if (x!=0) {z=y/x}
Weirder still that divide by zero generates an very low level interupt

[Cheif Operations Director]

19 minutes ago, K^2 said:

Yeah, but if you choose to say "one is a boy" or "one is a girl" after you saw the group, based on whether there is at least one of these, then we're back to 50/50. That's crucial.

Edit: Specifically, consider this setup. I walk on the street. I see a group with two children. I pick one child at random, if it's a boy, I say, "At least one is a boy." If it's a girl, I say "At least one is a girl". The choice is entirely random, and so it's not "first" or "older child" or any of that nonsense.

Do you agree that this is consistent with wording of the OP's problem? If not, then could you please clarify what the difference is? Could be purely linguistic disagreement. But if you agree that this setup is consistent with wording of the problem, it's trivial to show that in THIS setup, the other child can be a boy or a girl with 50/50 odds.

I concur as I said above

[YNM]

19 minutes ago, K^2 said:

Specifically, consider this setup. I walk on the street. I see a group with two children. I pick one child at random, if it's a boy, I say, "At least one is a boy." If it's a girl, I say "At least one is a girl". The choice is entirely random, and so it's not "first" or "older child" or any of that nonsense.

I'd say it's more like :

You walk about, and you see your friend holding two prams (just for ease)

You don't get to actually see the child first.

Then you asked "Oh, you had two kids ? wow !"

Then he replied "Oh, yeah ! One is a boy !"

Then the 4th wall closes and you got a question "what's the likelyhood the other child is also a boy ?"

Edited July 22, 2018 by YNM

[Cheif Operations Director]

1 minute ago, YNM said:

I'd say it's more like :

You walk about, and you see your friend holding two prams (just for ease)

You don't get to actually see the child first.

Then you asked "Oh, you had two kids ? wow !"

Then he replied "Oh, yeah ! One is a boy !"

Then the 4th wall closes and you got a question "what's the likelyhood the other child is also a boy ?"

Yes it's 50-50

[YNM]

5 minutes ago, magnemoe said:

again its an definition who is precise as long as you follow the rules. 

Maths is, in the end, also about consensus and agreements. Language again.

[Cheif Operations Director]

There are only two options (if you believe what the majority of society believes)

[YNM]

6 minutes ago, magnemoe said:

And for the 1/0=0 argument this is for computers not math

Why even brought that up then ?

Also,there's a reason why it' called computer language.

[Cheif Operations Director]

1. Boy

2. Girl

That is all there is this is not a probability puzzle.

[YNM]

4 minutes ago, Cheif Operations Director said:

Yes it's 50-50

Except it's not quite.

By quite a lot.

Consider if the two kids were fraternal twins - you'll see that in the case where one is of a certain gender it's far more likely for the other to be of the opposite gender.

But that can be extended to other siblings as well.

This has nothing to say that your next child will be more likely of a certain gender though.

Edited July 22, 2018 by YNM

[Cheif Operations Director]

This is like one of those fake video "IQ" test they either are dumb or prank you with some grammar or random clue because hidden in the placement of a comma

Just now, YNM said:

Except it's not quite.

By quite a lot.

Consider if the two kids were fraternal twins - you'll see that in the case where one is of a certain gender it's far more likely for the other to be of the opposite gender.

But that can be extended to other siblings as well.

This has nothing to say that your next child will be more likely of a certaij gender though.

Yes but those numbers are not calculable and not given

[YNM]

Just now, Cheif Operations Director said:

This is like one of those fake video "IQ" test they either are dumb or prank you with some grammar or random clue because hidden in the placement of a comma

duh, no it's not really.

But be it as you think it is.

[Cheif Operations Director]

These numbers are literally changed EVERY second 

Is also is not mentioned in the problem also! 

You can not take statistics that are not even given as a fact. 

You only have 2 options boy or girl a statement about the possibility of twins and such is not given in the statement.

[YNM]

2 minutes ago, Cheif Operations Director said:

You can not take statistics that are not even given as a fact. 

Probability isn't exactly statistics. Nor is the reverse.

But you can link the two, and it's a fairly powerful usable tool.

[Cheif Operations Director]

3 minutes ago, YNM said:

Probability isn't exactly statistics. Nor is the reverse.

But you can link the two, and it's a fairly powerful usable tool.

Probability is the result of statistics

If I say tell me right now will an asteroid collide with earth but gave you no STATISTICS/ numbers (which are derived from statistics) your chance of being right is 50/50

You are presented with statistics:

On 7/18/2018 at 4:01 AM, Gargamel said:

You are walking down the street, when you run into a friend of yours.  She has her two children with her.  One of them is a boy.  What are the odds that the other child is also a boy?

2 Children 1 is a boy the other is unknown.

the only two options are boy and girl

These are the statistics

So what is the probability that it will be a boy?

50% given that is the only statistic in all of this that is not changing every second. 

Edited July 22, 2018 by Cheif Operations Director

[YNM]

4 minutes ago, Cheif Operations Director said:

Probability is the result of statistics

So they had to actually test every dice for 1000 times ?

Good quality control there.

[Cheif Operations Director]

Just now, YNM said:

So they had to actually test every dice for 1000 times ?

Good quality control there.

Read what I said above

Rolling a dice (assuming it is fair) is the result of aerodynamics and gravity. If you set it up right you will land the same numbers every time.

[YNM]

Eh, I have better things to worry of anyway.

[Cheif Operations Director]

I'm not wrong

[K^2]

42 minutes ago, YNM said:

I'd say it's more like :

You walk about, and you see your friend holding two prams (just for ease)

You don't get to actually see the child first.

Then you asked "Oh, you had two kids ? wow !"

Then he replied "Oh, yeah ! One is a boy !"

Then the 4th wall closes and you got a question "what's the likelyhood the other child is also a boy ?"

And in this setup it's 50/50. Because if both are boys, he's guaranteed to tell you that one's a boy, but if one is a girl, it's a 50/50 chance. So you end up with a bias towards boy-boy that compensates for the fact that there are two permutations of boy-girl/girl-boy.

Id est, consider meeting 8 such individuals in a row. Two of each child combination BB, BG, GB, and GG. You'll get both BB parents tell you that one is a boy, and one of each BG and GB, giving you 4 total parents saying "one is a boy". Of these, the other is also a boy for 2 of them. That's half.

It's only if you know in advance that the parent would ALWAYS say "one is a boy" if they had one, then we end up 6 out of the above 8 parents in the "one is a boy" group. But that absolutely does not follow from OP's question. I'm not saying it's an invalid interpretation, but one that's no more valid than the 50/50 alternative that you just presented.

 

P.S. Had to look up what a "pram" is. In US, the term used is usually "stroller".

Edited July 22, 2018 by K^2

[Cheif Operations Director]

If anyone objects to the 50%-50% probability please provide an a counter instead of just saything "math!" or "grammar!" Please do not use data that changed every second either.

[Superfluous J]

2 hours ago, Cheif Operations Director said:

It's neutral

It's 50% anything else is illogical. Grammar does not apply here and we have only two options. It's like saying a house is over that  hill (boy) or it is not (girl) it 50% you may have a house or you may not. Birth rates are not statistly valid, they change every second, literally. With no other useful information what are we to deduct other than a 50% - 50% probability.

 

It doesn't work that way. You can say it's 50/50 here because it basically is but if humans reproduced in 1:9 ratios boys to girls, it'd be a 1:9 chance the other kid was a boy, not 1:1.

Edited July 22, 2018 by 5thHorseman

[Cheif Operations Director]

3 minutes ago, 5thHorseman said:

 

It doesn't work that way. You can say it's 50/50 here because it basically is but if humans reproduced in 1:9 ratios boys to girls, it'd be a 1:9 chance the other kid was a boy, not 1:1.

But they do not and the ratio is not fixed as people are born and die every second 

[Superfluous J]

4 hours ago, Cheif Operations Director said:

But they do not and the ratio is not fixed as people are born and die every second 

"We can't tell for sure so it must be 50/50" is not the correct way to logic.

I either have a laptop on my desk or a suitcase full of Aztec gold. But you can't tell from where you are and sometimes my laptop is not on my desk so therefore it must be 50/50.

[Tullius]

5 hours ago, Cheif Operations Director said:

If anyone objects to the 50%-50% probability please provide an a counter instead of just saything "math!" or "grammar!" Please do not use data that changed every second either.

If we agree that "one of them is a boy" means "at least one of them is a boy", we have the following:

case	kid A	kid B
1	girl	girl
2	boy	girl
3	girl	boy
4	boy	boy

So there are three cases, where the parent will say "one of them is a boy", but only one case, where the second kid is also a boy.

As we assume for simplicity that all cases are equally likely, the answer is 1/3.

The reason is that the boy is not identified, i.e. you don't know in which of the two prams the boy is (nor do you know anything else identifying the boy)

If the parent would point at a pram and say "this one contains a boy" (or he would just say "Joey is a boy"), the kid is identified (i.e. in terms of the table above, we have "kid A is a boy") and so the correct answer is 1/2.

[K^2]

10 minutes ago, 5thHorseman said:

"We can't tell for sure so it must be 50/50" is not the correct way to logic.

I either have a laptop on my desk or a suitcase full of Aztec gold. But you can't tell from where you are and sometimes my laptop is not on my desk so therefore it must be 50/50.

Devil's advocate: Technically, if we have NO other information, default is 50/50 as per Principle of Maximum Entropy. In general, if we have no constraints on probability distribution, uniform distribution is the most reasonable assumption. If you do have some information, distribution that maximizes entropy while maintaining constraints is the best guess. For example, if you know the mean and variance of some sample, normal distribution is a very good guess. As with anything in statistics, this doesn't work always, but simply more often than any alternative, yet it's a surprisingly powerful method, allowing to get very believable probability distributions when very little information is available. This approach is also used in signal processing and image enhancement.

Of course, this falls apart as soon as we start throwing additional information at it. I've just checked on my suitcase of Aztec gold, and since I have possession of it, and it being very unlikely that there are two such suitcases, I can adjust my estimate of probability of you having a suitcase full of Aztec gold to rather unlikely. Somebody with no prior knowledge of relative rarity of laptops vs Aztec gold would have to accept the 50/50 claim, however.

That's not to encourage turnings this into argument from ignorance, as we certainly have a wealth of statistical information on gender distribution across regions and age groups, and can always do better than 50/50 for this.