The Boy or Girl Paradox (riddle) (gtfih)

[hiimzac]

You are creating a DEPENDENT relationship by multiplying. This is an INDEPENDENT relationship.



No it's not. It's like saying, "you flipped 9 heads, what is the chance you flip heads on the 10th flip?" And guess what? It's still 50%.

no. it's not asking for a discrete probability on a single flip, it's asking for a probability distribution.

[mynameisuntz]

no, he's saying he already has 1 boy and is asking what the probability is that his OTHER child is also a boy. we know the answer is .25 by knowing the probability of getting two unique instances of a .5% chance

this **** aint hard

Dude, the second event is independent of the first event. The moment you look at other events to describe an INDEPENDENT event, you know you are wrong. The gender of the other child has zero bearing on the gender of the child in question because the gender of the child in question does not rely on ANYTHING outside of itself.

It is 50%.

no. it's not asking for a discrete probability on a single flip, it's asking for a probability distribution.

It's saying, "you have one boy, what's the other child going to be?"

Or

"You flipped heads once, what's the next flip going to be?"

No matter what, it's 50%.

Stop looking at trends; look at the individual trial in question.

[Mephisto91]

the funniest part about this thread is that dude insisting its .5 and saying **** like "zomg why i take math above grade 7 lol"

it's .25, it's a binomial distribution, yes the choice of each individual child being male is .5 but thats like saying you have a 50% chance to flip a coin ten times and get heads everytime.

bust out your ti-83 and do a cumulative density function fuark

Retard alert. It's not like saying that at all. It's like saying after already flipping a coin 9 times and getting heads, the chances that the next flip will be heads is still 50%. You're no less likely to get heads on one flip just because you got heads every time before, the coin doesn't have a mind of it's own and choose to make the probability even.

[hiimzac]

Dude, the second event is independent of the first event. The moment you look at other events to describe an INDEPENDENT event, you know you are wrong. The gender of the other child has zero bearing on the gender of the child in question because the gender of the child in question does not rely on ANYTHING outside of itself.

It is 50%.

Retard alert. It's not like saying that at all. It's like saying after already flipping a coin 9 times and getting heads, the chances that the next flip will be heads is still 50%. You're no less likely to get heads on one flip just because you got heads every time before, the coin doesn't have a mind of it's own and choose to make the probability even.

they are not independent events because they are probability distributions holy ****. the question says this: i flipped a coin 10 times, it came up heads at least 9 times, what is the probability the last flip was also heads? you'd do a cumulative density function and see that the prob of getting 10 heads is different from getting 9.

it's a binom distribution with x number of trials. x in this case is 2, probability is .5, the chances of getting greater than or equal to two successes in 2 trials with a .5 prob is .25

sorry if you never took stats

[84renzo]

its fukking 288 u ****s

[mynameisuntz]

they are not independent events because they are probability distributions holy ****. the question says this: i flipped a coin 10 times, it came up heads at least 9 times, what is the probability the last flip was also heads? you'd do a cumulative density function and see that the prob of getting 10 heads is different from getting 9.

it's a binom distribution with x number of trials. x in this case is 2, probability is .5, the chances of getting greater than or equal to two successes in 2 trials with a .5 prob is .25

sorry if you never took stats

I did take stats. I'm going to grad school soon, too, where I'll be re-doing stats and research methods allllllll over again.

You're still wrong. You can flip a coin and get heads a billion times, and the chance of you flipping heads the next flip is still 50%. I really have no idea how you can argue the contrary.

It seems like you're arguing for the odds of flipping heads 10 times in a row, which is obviously not 50%. But the odds of hitting heads on any individual flip regardless of other events will always be 50%. Always.

[hiimzac]

i mean ffs the guy even worded it as "what is the probability the other one is a boy". the probability of getting 2 successes with distinct probabilities of .5 each is .25...how is this hard

[Ka0s]

i mean ffs the guy even worded it as "what is the probability the other one is a boy". the probability of getting 2 successes with distinct probabilities of .5 each is .25...how is this hard

He didn't ask what is the chance of having 2 boys

[Mephisto91]

no, he's saying he already has 1 boy and is asking what the probability is that his OTHER child is also a boy. we know the answer is .25 by knowing the probability of getting two unique instances of a .5% chance

this **** aint hard

Do you even read? The word "also" is not in the question. Here is the exact question: "What is the probability that the other child is a boy?" not "What is the probability both children are boys?" or "What is the probability that the other child is ALSO a boy" like you seem to be reading out of nowhere.

That's why it's called a riddle when it really isn't. Idiots like you will assume that the beginning of the question actually has something to do with the basic question a 3 year old could answer.


I wonder what it's like for the people who are this dumb just going about their day. Every step must be like a brand new world.

[mynameisuntz]

i mean ffs the guy even worded it as "what is the probability the other one is a boy". the probability of getting 2 successes with distinct probabilities of .5 each is .25...how is this hard

The probability of getting one boy, then another boy when no children have been born = 25%
The odds of the second child being a boy when the first is born a boy = 50%

[feelymcfeel]

Boy/Boy
Boy/Girl
Girl/Boy
Girl/Girl

We know at least one is a boy so the Girl/Girl is gone leaving us with 3 possible choices--33.3% chance that the combination is Boy/Boy

/thread

[iceypain]

they are not independent events because they are probability distributions holy ****. the question says this: i flipped a coin 10 times, it came up heads at least 9 times, what is the probability the last flip was also heads? you'd do a cumulative density function and see that the prob of getting 10 heads is different from getting 9.

it's a binom distribution with x number of trials. x in this case is 2, probability is .5, the chances of getting greater than or equal to two successes in 2 trials with a .5 prob is .25

sorry if you never took stats

it's definitely not 1/4 brah. I think that there's an argument for 1/3 though.

an analogous question: if I flip two coins simultaneously and tell you that at least one is heads, what is the probability that the other one is heads also?

see even though the each coin is independent of the other, the overall outcome is not necessarily the same because it's not a sequence.

[Ka0s]

The probability of getting two boys when no children have been born = 25%
The odds of the second child being a boy when the first is born a boy = 50%

This

[Mephisto91]

they are not independent events because they are probability distributions holy ****. the question says this: i flipped a coin 10 times, it came up heads at least 9 times, what is the probability the last flip was also heads? you'd do a cumulative density function and see that the prob of getting 10 heads is different from getting 9.

it's a binom distribution with x number of trials. x in this case is 2, probability is .5, the chances of getting greater than or equal to two successes in 2 trials with a .5 prob is .25

sorry if you never took stats

Do you see the word "also" in OPs question? I love how people rewrite the question in their heads and then tell us the actual question is wrong.

[hiimzac]

I did take stats. I'm going to grad school soon, too, where I'll be re-doing stats and research methods allllllll over again.

You're still wrong. You can flip a coin and get heads a billion times, and the chance of you flipping heads the next flip is still 50%.

ok then you should be able to follow this

the bolded is where you **** up. the probability of every individual flip is .5, but when trying to assess the probability of getting x number of successes in y number of trials (in this case, a boy being considered a success, x being 2, and y being 2) we need to create a probability distribution.

surely you understand that the more times we flip a coin the closer and closer the actual results will be to the expected (ie half heads half tails) (if you can't understand this you lied to me and never took stats). to flip a coin 100 times and get 90 of them as heads we would immediately assume something is wrong because getting 90 heads is way less likely in 100 trials than getting somewhere around 50. the point is that the probability of x number of successes in y trials is obviously going to vary...

[mynameisuntz]

/thread

Then respond:

This. To everyone saying 1/3 - why do you make BG/GB two separate scenarios when really they are one in the same? You have one boy, he is older or younger than the sibling in question. Order, age, it doesn't matter. It is:

(BB) or (GB or BG) where each set of parentheses = one possible outcome. In the former, the non-original sibling = boy, in the latter, the non-original sibling = girl. It's 50/50.

"I have a son, can you guess what my other child is?"
A) An older son.
B) A younger son.
C) An older daughter.
D) A younger daughter.

We don't differentiate age between A and B, yet we do for C and D. Why? Really it's (A or B) or (C or D). One or the other set of scenarios.

[Mr.Roarke]

100%

He said he had two children. And he said atleast one is a boy. You don't say that if theres only one boy

[mynameisuntz]

ok then you should be able to follow this

the bolded is where you **** up. the probability of every individual flip is .5, but when trying to assess the probability of getting x number of successes in y number of trials (in this case, a boy being considered a success, x being 2, and y being 2) we need to create a probability distribution.

surely you understand that the more times we flip a coin the closer and closer the actual results will be to the expected (ie half heads half tails) (if you can't understand this you lied to me and never took stats). to flip a coin 100 times and get 90 of them as heads we would immediately assume something is wrong because getting 90 heads is way less likely in 100 trials than getting somewhere around 50. the point is that the probability of x number of successes in y trials is obviously going to vary...

I understand what regression to the mean is, but you're now committing gambler's fallacy or very close to something like it.

Each individual trial is independent of other trials. Hitting heads in one trial, regardless of all the other trials that have led up to this trial, will always be 50%. Always. Go ask a stats teacher, "will getting heads always be 50% regardless of how many flips it has landed heads prior?"

[Lailoken]

they are not independent events because they are probability distributions holy ****. the question says this: i flipped a coin 10 times, it came up heads at least 9 times, what is the probability the last flip was also heads? you'd do a cumulative density function and see that the prob of getting 10 heads is different from getting 9.

it's a binom distribution with x number of trials. x in this case is 2, probability is .5, the chances of getting greater than or equal to two successes in 2 trials with a .5 prob is .25

sorry if you never took stats

this is my thinking when I arrived at .25.

if you are betting money on a coin toss, how many times does the coin have to land on heads before you wise up and realize it's probably going to be tails next flip? it was common sense for me long before I learned the mathematical reasoning behind it. maybe the misc doesn't gamble enough.

brb flipping heads 9 times in a row and thinking "herp derp hey it's 50/50 odds still independet herp derp might as well bet on heads again right?"

[notriceagain]

this is in no way a paradox

[hiimzac]

The probability of getting one boy, then another boy when no children have been born = 25%
The odds of the second child being a boy when the first is born a boy = 50%

discrete probability of that single instance is .5. if you wanted to do a cumulative density function of that it'd be 1 trial, .5 chance of success, looking for 1 or more successes. you'd get .5. then when you consider there are 2 children involved it's now 2 trials, .5 chance of success, looking for 2 successes which is a different probability entirely.

you're going to struggle with research methods, i think ;x

[Ka0s]

Yo I already destroyed this thread on first page

Pr(One son being boy|Other son being boy) = Pr(One son being boy) = 50%

Why are we even arguing past this

[TranKy]

The question is equivalent to ' what is the chance of him having 2 boys given that he does (must ) not have 2 girls ? '

When you state : 'he has at least 1 boy, you already make the "independant" assumption false '

The answer is : 1/3 % .

[southeastoz]

Facepalming at those saying anything but 50% (except the cheeky ones who include the small 49/51% discrepancy in male/female pop).

[Ka0s]

this is my thinking when I arrived at .25.

if you are betting money on a coin toss, how many times does the coin have to land on heads before you wise up and realize it's probably going to be tails next flip? it was common sense for me long before I learned the mathematical reasoning behind it. maybe the misc doesn't gamble enough.

brb flipping heads 9 times in a row and thinking "herp derp hey it's 50/50 odds still independet herp derp might as well bet on heads again right?"

Lmfao

[Ka0s]

The question is equivalent to ' what is the chance of him having 2 boys given that he does (must ) not have 2 girls ? '

When you state : 'he has at least 1 boy, you already make the "independant" assumption false '

The answer is : 1/3 % .

That is not the question at all

[mynameisuntz]

discrete probability of that single instance is .5. if you wanted to do a cumulative density function of that it'd be 1 trial, .5 chance of success, looking for 1 or more successes. you'd get .5. then when you consider there are 2 children involved it's now 2 trials, .5 chance of success, looking for 2 successes which is a different probability entirely.

you're going to struggle with research methods, i think ;x

I did not struggle with research methods at your age and I won't in grad school. You are committing gambler's fallacy and allowing other trials sway your judgment of individual trials. The idea of a certain outcome being "due" is what you are saying.

A coin flip is independent of other coin flips. It is always 50/50 for heads or tails. Always. If you're going to look at 100 trials at once, then it's different. But a SINGLE trial will always be independent from all other trials, and it will always be 50/50.

this is my thinking when I arrived at .25.

if you are betting money on a coin toss, how many times does the coin have to land on heads before you wise up and realize it's probably going to be tails next flip? it was common sense for me long before I learned the mathematical reasoning behind it. maybe the misc doesn't gamble enough.

brb flipping heads 9 times in a row and thinking "herp derp hey it's 50/50 odds still independet herp derp might as well bet on heads again right?"

You are both committing gambler's fallacy, congratulations.

"For example, if a fair coin is tossed repeatedly and tails comes up a larger number of times than is expected, a gambler may incorrectly believe that this means that heads is more likely in future tosses.[3] Such an expectation could be mistakenly referred to as being due, and it probably arises from everyday experiences with nonrandom events (such as when a scheduled train is late, where it can be expected that it has a greater chance of arriving the later it gets). This is an informal fallacy. It is also known colloquially as the law of averages.

What is true instead are the law of large numbers – in the long term, averages of independent trials will tend to approach the expected value, even though individual trials are independent – and regression toward the mean, namely that a rare extreme event (say, a run of 10 heads) is less likely that it may be perceived to be, and that an expectation of a similar extreme is likely to be disappointed in favor of a more representative pattern.

The gambler's fallacy implicitly involves an assertion of negative correlation between trials of the random process and therefore involves a denial of the exchangeability of outcomes of the random process. In other words, one implicitly assigns a higher chance of occurrence to an event even though from the point of view of "nature" or the "experiment", all such events are equally probable (or distributed in a known way)."

[Ka0s]

Yes, dat

http://en.wikipedia.org/wiki/Law_of_averages

Belief that an event is "due" to happen: For example, "The roulette wheel has landed on red in three consecutive spins. The law of averages says it's due to land on black!" Of course, the wheel has no memory and its probabilities do not change according to past results

[iceypain]

Yo I already destroyed this thread on first page

Pr(One son being boy|Other son being boy) = Pr(One son being boy) = 50%

Why are we even arguing past this

how i interpret it is that this is correct if the second child is born after the question is posed.

[Mephisto91]

Yes, dat

http://en.wikipedia.org/wiki/Law_of_averages

Belief that an event is "due" to happen: For example, "The roulette wheel has landed on red in three consecutive spins. The law of averages says it's due to land on black!" Of course, the wheel has no memory and its probabilities do not change according to past results

/thread if the retards can understand it. They seem to be having a hard time with all the other explanations though.