Thread 16790153

>P(2 boys | Mary says she has a boy) = P(2 boys)/P(Mary says she has a boy) = 1/(4 P(Mary says she has a boy))

>Now P(Mary says she has a boy) = 1/4P(Mary says she has a boy | Mary has 2 boys) + 1/2P(Mary says she has a boy | Mary has 1 boy & 1 girl)

>We can assume P(Mary says she has a boy | Mary has 2 boys) = 1 if we consider Mary to always say the truth, which is reasonable.

>Assume P(Mary says she has a boy | Mary has 1 boy.& 1 girl) = 1/2 because yes?

>So P(Mary says she has a boy) = 1/2 which is quite expected for symmetry

>Therefore P(2 boys | Mary says she has a boy) = 1/2

Am I a retard? Everybody on Reddit is arguing over this

ur reteard
no extra info -> 4 cases: bb, bg, gg, gb. gg is forbidden. 3 cases left with 2 of 3 including a boy.

weekday given: there are 7×7=49 possible weekday of birth combos for 2 children.
with 2 genders that's again 4 combos.
of those 196 cases there are 14 cases were the first born is a girl and 14 cases were the second is a girl. both being born on tuesday is the same case so the sum is 27 instead of 28. 14 of those 27 cases have a boy and that around 51.85%.

>>16790153 (OP)
Weird how adding a seemingly irrelevant piece of information alters the probability, huh? Suddenly you have an extra variable to account for and the extra information rules out some combinations. If that feels absurd, get a load of this:
https://en.wikipedia.org/wiki/Raven_paradox

>>16790308
For the first case you assume that her having a boy would immediately imply her saying she has a boy, so you assume P(Mary says she has a boy | Mary has a boy, and eventually a girl) = 1 which is just an assumption (as it's mine to say that this probability is 1/2 when she has both a boy and a girl)

For the second case there is no way the birth day influences the probability. They are independent events. She could have said "I have a boy and throwing a 7 faces die gave me 2" and it's literally the same thing. Where's the difference?

>>16790332
>She could have said "I have a boy and throwing a 7 faces die gave me 2" and it's literally the same thing
Yep. See >>16790322

What's her relationship with her father like? Does she feel safe and stable? These things have been found to alter the probability of a woman having a boy or a girl.

>alter the probability of a woman having a boy or a girl.
The year is 2025 and fucktards still don't understand conditional probability. Funny how you're smart enough to realize you can replace the weekday element with a die-roll outcome, but not smart enough to go all the way and replace the boy/girl element with a random coin flip. That way you end up with a prompt your "mind" has been conditioned to work with correctly by public schooling. :^)

>>16790364
I mean you're literally demonstrating how irrelevant information alters the priors getting confused by the red herring of birth as a biological outcome.

>>16790344
I do know the raven paradox. However, I'm not sure how that's relevant here

What if she said "I have a boy and throwing a 1010-face dice I got a 1"? Also it isn't really relevant the fact that she did in fact threw the dice, she could just say "I have a boy and I thought about the random number 29429"

I'm pretty sure these don't change the probability, there's just a way to rephrase the problem in such a way that it looks like it actually does.

>>16790364
I'm just discussing the problem as I've found it. Thinking about coin flips instead of babies born doesn't give me any more insight

>>16790364
Sometimes I really wonder what makes anons like this tick. Who seethes this much on a mathematics post on the science and mathematics board?

>>16790364
>I allow irrelevant information to alter the ontology of a fixed probability outcome in order to comply with le bayes theorem
>This makes me smart
It's an independent event with a 50% probability. No different than a coin flip being 50/50 regardless of getting a heads previously. Don't rant about "muh 2 boys born on Tuesdays produces one permutation but order matters for all the rest" drivel because I'm not going to read it.

>>16790153 (OP)
Original video is wrong, else they misquoted.

There isn't a prior constraint affecting values, it is 50% or if you want something more technical, the background chance of having a girl.

>>16790633
Statfags genuinely believe that knowing the birthday of one child changes the probability because building a permutation table of older and younger siblings yields the possibility of 2 tuesday born boys. The rest of the outcomes are given order dependent outcomes (e.g. older brother on a tuesday and younger sister on a tuesday can be reversed for the sister to be older), but because the notation of older and younger brothers born on Tuesdays would be the same, they "can't be reversed without being identical." An ounce of critical thinking debunks this because it implies that only one of the order dependent outcomes states that their genomes are identical (if you were to use DD/MM/YY notation the logic falls apart).

My biostatistics professor included this as a trick question on an exam during my grad studies and it was really funny to watch the math virgins have a melty when the accepted answer was 50%

>>16790642
Your spergout over mathfaggotry and critical thinking is exactly the reason you can immediately exclude the possibility both sons were born on a Tuesday. Not a single layman would ever say "I have one son born on Tuesday" when they really have two sons both born on Tuesdays, they would say "at least one" or "both." Saying "I have one" is best-kind-of-correct logicfaggotry.

>>16790661
The actual problem with the question is that a real person would select a child at random uniformly and tell you their gender and day of birth (which makes the events independent and gives 50/50 odds). The correct phrasing for this question to make it give the 51.8% without ambiguity would be to say something like "Mary has two children, she is asked if at least one of them is a boy born on tuesday, and she replies yes."

>>16790669
Exactly. Honest rationality doesn't need the contrivance of a simulation or whatever thousand other forms of creation argument. Where rephrasing can isolate a proper question, tricking a bunch of grade schoolers with word problems is disingenuous to accurate records of intuition.

>>16790669
>>16790674
The same midwit psychopaths who attempt to trick idiots into abandoning basic critical thinking to get a poorly worded math problem "right" will also force you to spend $3,000 taking a class about how ever having children and accepting their biological sex in the first place is an act of bigoted enslavement, and if you don't take the class you can't graduate. They use statistical manipulation of resource use distribution and tell you to ignore jevons paradox to convince you that human procreation is the reason for the planet's ecological crisis, while the data centers powering the robots that will scream 51.85% into the void use the same amount of energy and water as millions of homes. They want to select against intuition and critical thinking, get everyone to take the words of hallucinating algorithms and illogical virgins as gospel and select for a weak and unwise populace. But why? This question, if you know of the demographic transition model theory, is rhetorical of course. Ted K was right in almost every way

>>16790682
chadgpt didn't pick 51.8% though and explained all sides

>>16790669
Exactly, this is what I thought to begin with. That's why assume P(Mary says she has a boy | Mary has a boy & a girl) = 1/2. Which I think is the most reasonable assumption, given this much info

>problem setup adds two extra random variables and two extra dimensions to the outcome's state space
>condition ties the sex variable to the day variable
>it carves chunks out of the state space in an asymmetric way
Yep, it's gonna be another episode of word thinkers getting filtered by conditional probability. And they're all gonna shit out paragraphs to explain why getting filtered means they're smarter. At least find some new ways and original of getting filtered by it instead of always making the same errors.

The tuesday is irrelevant information, obviously, unless you're presuming the reader knows statistical data of the current year the problem takes place in and the probability distribution curve of babies in days of the week, which is inane and ridiculous to consider.
Analytically speaking, there are four outcomes that could have happened:
The mother has Baby 1, 50% chance (simplifying) it's a boy or a girl. Baby 2, same chance, 50%.
There's four possible versions of events, Baby 1 was male, or female, which I'll write 1B or 1F, and same with Baby 2. So we're left with the only possibilities 1B 2B, 1B 2F, 1F 2B, and 1F 2F.
If we assume the mother is truthful, then that means the only case which has been defined as impossible is 1F 2F. There are 3 scenarios which would be compatible with the question of "Mary says she has a boy", 1B 2B, 1B 2F, and 1F 2B. Therefore, there's 2 out of 3 outcomes which involve one girl, so there's a 66.66% chance one of the babies is a girl.

This is literally just the fucking silver/gold coin problem repackaged with babies, you people need to get fucking real

>>16790801
See >>16790800
>it's gonna be another episode of word thinkers getting filtered by conditional probability. And they're all gonna shit out paragraphs to explain why getting filtered means they're smarter.

>>16790153 (OP)
Just ask yourself "how would I do this one billion times" and throw away "conditional probability thinking" and you'll be fine.

>>16790153 (OP)
Let's use Bayes.
P(2 boys | 1 boy born on Tuesday)= P(1 boy boT|2 boys)*P(2 boys)/P(1 boy boT)=(1/7)*(1/4)/((3/4)*(1/7)=1/3.
33.3%.
She really should have said that her FIRSTBORN was a boy, then she'd have had a nice 50% of having an other boy.
But maybe she wanted a baby girl, who's to say.

>>16790809
It's 14/27 =~ 0.518518518 using cardinalities (computed in {girl,boy}^2 x {1,2,3,4,5,6,7}^2).

>>16790802
Ok, I had posted without reading anything, but now I've re-read your post and decided to take a closer look. I did indeed get filtered by not thinking about it.
Note I have no formal learning on anything math past highschool, I certainly didn't study probability, but I know excel.

I plotted out the ENTIRE room of possibilities, with the nomenclature being x(B/G)y, where B is boy, G is girl, y is for baby 1 or baby 2, and x is the day the baby was born out of the week (Starting with Sunday as 1, Sat as 7, and critically Tuesday as 3)

Plotting out the whole tables, and eliminating every possibility that WAS NOT at least 1 boy being born on a tuesday, as Mary says, the answer is 13 events where Boy-boy, and 14 events between boy-girl and girl-boy. The answer then is clear as day: 14/27, or 51.851851..%
I've indeed been had, and now I really look like a fool. But, where exactly is the debate? This looks completely irrefutable and clear cut.

>>16790819
>where exactly is the debate?
Among people who think they can just talk their way into being right instead of doing what this guy did >>16790308 or at least what you did.

>>16790322
Interesting paradox. I've never heard of this. The solution is easy. The contrapositive cannot have the same truth value as the original proposition. In other words the law of excluded middle is the problem. It creates other paradoxes in logic such as the liar paradox. This shouldn't be puzzling to people.

>>16790828
More word-thinker nonsense.

>>16790819
The important thing is that you understand that understanding probabilities and other sciency stuff isn't trivial or even easy.

>>16790876
>The important thing is that you understand that understanding probabilities and other sciency stuff isn't trivial or even easy.
That's not important for him to understand. It's important for "scientists" to understand, but they're not exactly incentivized to do so.

>>16790879
They actually are or they get dunked on by colleagues.

>>16790892
Most of their colleagues are equally ignorant. The unstated rule in these circles is that you don't call others out, lest you be called out.

>>16790153 (OP)
it's 13 / 27

>>16790308
>both being born on tuesday is the same case
Wut? No it's not.

>>16790819
>All pairs are reversible permutations
>Except 2 boys born on Tuesdays
>Look I even put it in a spreadsheet
Bayestards are unsalvageably stupid

>>16790825
>talk your way into being right
Listing 2 boys born on Tuesdays as the only non-reversable option to skew the statistics is talking your way into being right using variable nomenclature. The events are independent, and the biological reality is that children have a 50% chance of being male or female. You're projecting and stupid

>>16791022
>events are independent
Correct: true by axiom. I can gift you a second or third daughter as a reward. 100% vector sum

>>16791022
>>16791021
A bunch of meaningless word salad. Word "thinkers" are biological LLMs.

>>16790153 (OP)
using math to model or simulate reality is fine as long as you understand the limitations or specifics where it makes sense.

>you have a bag of coins, you pulled X coin, what is the probability of pulling Y coin?
this is the case where first pull altered the odds. you have to use conditional probability
>you have three doors, behind one is reward, the tv anchor showed you that the door you did not pick doesnt have it, do you take the other doors?
again, the pull altered the odds, conditional probability
>woman had 2 babies, what are the odds of both of them being girls if first is a girl?
there isnt any (yet) proven pattern in universe picking boy/girl/herm yet, so you have two options: shut off your brain and apply same formula, essentially claiming there is finite series of girls and boys and since the mother already pulled one girl out of the bag, the odds of having 2nd one is higher or lower, depending on how you phrase the question

or

you refuse to play this game and say that the two events are not conditional and its not conditional probability. but that will lower your math score in test. after all they train us in schools to follow protocols and authorities, not to actually think.

P&A

>>16790153 (OP)
The problem is underspecified. We don't know if by "one" they mean "at least one" or "exactly one". I define that I'm going to go with the latter, then the answer is 50%.

>>16791022
>children have a 50% chance of being male or female
Not exactly, no.

>>16790800
>>16790308
Consider this problem:
>Mary has two children. She tells you that one is a boy born on the 20,000th microsecond of the day. What are the odds the other child is a girl?
Now I am sure you will say the odds are:
There are 86,400,000,000 microseconds in a day. Let this number be T. Let's assume the odds of being born on any given microsecond are uniform.
Birth order is not a variable, but order still matters, so, considering a decision-space of [math] T^2 [/math] there are [math] T [/math] opportunities to be born on the 20,000th microsecond for the first child and equally so for the second, however that combination of both boys being born on the 20,000th microsecond overlap, so there are [math] 2T-1 [/math] ways to have two boys with at least one born on the 20,000th microsecond.
There is no overlap for boy-girl, (BG [math] \neq [/math] GB), so there are 2T ways to have a boy and a girl.
Therefore the odds of having a girl are:
[math] \frac{2T}{(2T+2T-1)} = \frac{2T}{4T-1}=\frac{2}{4-1/T} = 0.5000000000028935[/math]
Wow. We should be thankful Mary did not mention which nanosecond!

>>16791312
>erm ackchewally there's a global bias toward 50.1% male births because of le socioeconomic factors
I would acknowledge this cope if this was your position, but we both know it isn't

>>16790332
>>16791015
There are no words that can describe accurately how much i despise retards like you.
>>16791320
> odds of having a girl
Is reading too hard for you, kiddo?

>>16790819
People's brains have a hard time telling apart more complex problems from nonsense or noise. It is necessary to put away gut feelings, and do the work to think rationally. Several manipulation and deception techniques rely on this fact.

It's 50/50. Either it's a girl or it isn't.