Poll: A women has two kids, one is a boy, what are the odds the other is also a boy?

[Avatar Roku]

TRICKEY!!!

Look, the options are:
(in order of birth)
Girl then Boy
Boy, then Girl
Boy, then Boy
Girl, then Girl

what is the chance that at least one kid is male? 75%, leaving us with 3 options.

1, both are boys
2, the 2nd kid was designated boy, however the first is girl
3, the 1st kid was designated boy, however the second is girl

there is a 33% chance.

The options at the start can be organised like this.

B - B 25%
B - G 25%
G - B 25%
G - G 25%

At least one of them is a boy.

B - B 33%
B - G 33%
G - B 33%
G - G 0%

Thus, the probability of the other sibling being a boy is 33%

No, the first birth has absolutely no bearing on the second, they're independent. 50%. If it was worded "What is the probability that a woman's two children are male", then you would be right, but it's worded "Her first child is male, what's the probability the second will be male?"

 

[SimuLord]

Think of the problem this way:
Instead of thinking "one is a boy" think "they are not both girls". Both mean the same thing.
If they are not both girls, then obviously there is a 33% chance that they are both boys.

The reason most people think that its 50% is because they interpret "one is a boy" as "the first one is a boy". That's not what it means. It means that at least one is a boy, but its still equally likely that it could be either, and half as likely that it could be both.

Not so. It said "what are the odds that the other is ALSO a boy"...in other words "what's the probability that the second child is a boy GIVEN that the first child is a boy?" The first child's gender is event A. The second child's gender is event B. Events A and B are independent.

Therefore P(B) = P (B|A) = 50%.

 

[SwitchShift]

The original post doesn't mention whether it is the older or younger sibling who is a boy, it could be either. I must admit I'm confused about variable probability, it is less likely to have two boys than a boy and a girl, but knowing the gender of one does not change the chances of the the gender of the other. It seems to me that the answer that the odds are 50% that the other kid is a boy, but 33% that the woman will have a two boy family if one kid is a boy (it has to be so, or else the 33% chance wouldn't be).

 

[Azraellod]

No, the first birth has absolutely no bearing on the second, they're independent. 50%. If it was worded "What is the probability that a woman's two children are male", then you would be right, but it's worded "Her first child is male, what's the probability the second will be male?"

It doesn't state which child is male. It could be the first born or the second born.

Edit: Sorry, misunderstood your reasoning, but you misread the question.

 

[Jerious1154]

Think of the problem this way:
Instead of thinking "one is a boy" think "they are not both girls". Both mean the same thing.
If they are not both girls, then obviously there is a 33% chance that they are both boys.

The reason most people think that its 50% is because they interpret "one is a boy" as "the first one is a boy". That's not what it means. It means that at least one is a boy, but its still equally likely that it could be either, and half as likely that it could be both.

Not so. It said "what are the odds that the other is ALSO a boy"...in other words "what's the probability that the second child is a boy GIVEN that the first child is a boy?" The first child's gender is event A. The second child's gender is event B. Events A and B are independent.

Therefore P(B) = P (B|A) = 50%.

I reread the question, and I think you're right according to the phrasing. The way I first saw it written when I had it explained to me was "one is a boy, what are the odds that they are both boys?" In that case, the answer is 33%.

 

[Avatar Roku]

No, the first birth has absolutely no bearing on the second, they're independent. 50%. If it was worded "What is the probability that a woman's two children are male", then you would be right, but it's worded "Her first child is male, what's the probability the second will be male?"

It doesn't state which child is male. It could be the first born or the second born.

Edit: Sorry, misunderstood your reasoning, but you misread the question.

No, read it again. "One is a boy, what is the probability the other is also a boy?" In other words, the one we know is male may as well not even exist as far as the question goes, it's just asking about the other.

 

[SimuLord]

Think of the problem this way:
Instead of thinking "one is a boy" think "they are not both girls". Both mean the same thing.
If they are not both girls, then obviously there is a 33% chance that they are both boys.

The reason most people think that its 50% is because they interpret "one is a boy" as "the first one is a boy". That's not what it means. It means that at least one is a boy, but its still equally likely that it could be either, and half as likely that it could be both.

Not so. It said "what are the odds that the other is ALSO a boy"...in other words "what's the probability that the second child is a boy GIVEN that the first child is a boy?" The first child's gender is event A. The second child's gender is event B. Events A and B are independent.

Therefore P(B) = P (B|A) = 50%.

I reread the question, and I think you're right according to the phrasing. The way I first saw it written when I had it explained to me was "one is a boy, what are the odds that they are both boys?" In that case, the answer is 33%.

If you say 33% to that construction, you're using "one is a boy" as your sample space. The odds that they are BOTH boys if ONE is a boy is asking P (X=2|X=1), which is zero. If one is a boy, two cannot be boys. It's still not 33%.

The odds that AT LEAST one child is a boy is 75%. P(X>=1)=3/4.

There are no constructions here that would make the sample space such as to make the probability 33%.

 

[Azraellod]

No, read it again. "One is a boy, what is the probability the other is also a boy. In other words, the one we know is male may as well not even exist as far as the question goes, it's just asking about the other.

I did.

It states at least one is a boy. It doesn't state which one is the boy. If it were to state which of the two siblings was the boy, then you would be correct, but since it doesn't, it can be either sibling.

 

[Avatar Roku]

Think of the problem this way:
Instead of thinking "one is a boy" think "they are not both girls". Both mean the same thing.
If they are not both girls, then obviously there is a 33% chance that they are both boys.

The reason most people think that its 50% is because they interpret "one is a boy" as "the first one is a boy". That's not what it means. It means that at least one is a boy, but its still equally likely that it could be either, and half as likely that it could be both.

Not so. It said "what are the odds that the other is ALSO a boy"...in other words "what's the probability that the second child is a boy GIVEN that the first child is a boy?" The first child's gender is event A. The second child's gender is event B. Events A and B are independent.

Therefore P(B) = P (B|A) = 50%.

I reread the question, and I think you're right according to the phrasing. The way I first saw it written when I had it explained to me was "one is a boy, what are the odds that they are both boys?" In that case, the answer is 33%.

If you say 33% to that construction, you're using "one is a boy" as your sample space. The odds that they are BOTH boys if ONE is a boy is asking P (X=2|X=1), which is zero. If one is a boy, two cannot be boys. It's still not 33%.

The odds that AT LEAST one child is a boy is 75%. P(X>=1)=3/4.

There are no constructions here that would make the sample space such as to make the probability 33%.

Wait, if the given is that one is boy, wouldn't the odds that at least one is a boy be 100%?

 

[Gmano]

It occurs to me that the question is a little bit tricky for some.

If one takes the order into account, we bring chance to 50%
If the birth order is not taken into account, we get 33%

 

[Avatar Roku]

No, read it again. "One is a boy, what is the probability the other is also a boy. In other words, the one we know is male may as well not even exist as far as the question goes, it's just asking about the other.

I did.

It states at least one is a boy. It doesn't state which one is the boy. If it were to state which of the two siblings was the boy, then you would be correct, but since it doesn't, it can be either sibling.

So yeah, it can be either the first or the second, but that doesn't change the answer. Again, the one we know is a boy may as well not exist, as him being a boy has no bearing whatsoever on whether the other one is a boy. It has a bearing on whether they're both boys, but not on whether or not the other is.

 

[NeutralDrow]

50%.

The question isn't about the odds that both children are boys. Maybe if it were phrased more carefully, but as is, it's asking what the odds are that one given child is a boy.

 

[QuantumSteve]

No, the first birth has absolutely no bearing on the second, they're independent. 50%. If it was worded "What is the probability that a woman's two children are male", then you would be right, but it's worded "Her first child is male, what's the probability the second will be male?"

50%.
The question isn't about the odds that both children are boys. Maybe if it were phrased more carefully, but as is, it's asking what the odds are that one given child is a boy.

So yeah, it can be either the first or the second, but that doesn't change the answer. Again, the one we know is a boy may as well not exist, as him being a boy has no bearing whatsoever on whether the other one is a boy. It has a bearing on whether they're both boys, but not on whether or not the other is.

We know the one child is a boy, this is conditional. Any other boy with a sister cannot be this this boy's brother. Conversely, any girl with a sister cannot be this boy's sister.

Knowing the gender of one of the children limits the sets that the pair can belong to, and therefore alters the probability of the other child.

 

[Azraellod]

So yeah, it can be either the first or the second, but that doesn't change the answer. Again, the one we know is a boy may as well not exist, as him being a boy has no bearing whatsoever on whether the other one is a boy. It has a bearing on whether they're both boys, but not on whether or not the other is.

Because we do not know which of the two children it the boy, we have to start from the beginning in order to work out the probability, and that means reverting to the reasoning posted earlier.

Spoiler: Tree Diagram

You are assuming that we already know the child to be judged first is definitely a boy, so you're starting in the wrong place.

 

[UsefulPlayer 1]

I don't think the question is phrased correctly. I'm pretty sure it went something like this, "A woman has a baby and it is a boy. What are the chances that her next child is also a boy?"

To which I would answer, "50%"

 

[Johnson McGee]

one of the births has been set, the other is variable.

once a choice is set, it has no effect on probability. Therefore answer is 50%

alternately, to those arguing it has to be 33% since there are 4 options to start with and one is eliminated: the question does not ask the odds of the first or second being a boy, just that one of them is. Therefore boy/girl and girl/boy are the same option, you start with 3 options, setting one as boy eliminates one and now you have 1/2 choices = 50% again. (permutations vs. combinations, look it up if you don't know)

The answer would be 33% if it was asking the odds of the first or last one (specifically) being a girl.

 

[Avatar Roku]

So yeah, it can be either the first or the second, but that doesn't change the answer. Again, the one we know is a boy may as well not exist, as him being a boy has no bearing whatsoever on whether the other one is a boy. It has a bearing on whether they're both boys, but not on whether or not the other is.

Because we do not know which of the two children it the boy, we have to start from the beginning in order to work out the probability, and that means reverting to the reasoning posted earlier.

Spoiler: Tree Diagram

You are assuming that we already know the child to be judged first is definitely a boy, so you're starting in the wrong place.

Problem with that tree diagram is, as you're so fond of pointing out, the order doesn't matter. So, let's use that diagram, call "H" Boy, call "T" Girl. Obviously, TT is out. That leaves us with three options: HH, HT, TH. Thing is, since order doesn't matter, HT and TH are the same thing, reducing our options to two, only one of which is the thing we're finding the probability of. Therefore, 50%.

 

[muckinscavitch]

Very straightforward, the gender of the second baby is not affected by the gender of the first child. So 50%. Had the question been "What are the chances of having two more boys?" then it would be 25% (.5*.5), but since one boy was already had, it does not enter into the equation.

Statistically though, the chance would be closer 48% since the world's population is between 49 and 48% men and 51-52% women, this is due to some biochemical happenings with added shit such as oestrogen and other hormones and such in our food...

 

[jonnosferatu]

As noted by Wikipedia, the question is uselessly ambiguous; 50% and 33% are both valid answers.

Thus, those of you who "cleverly deduced" 33% need to get off your high horses and stop making flawed assumptions. The same, sans high horse comment, applies to the 50% crowd.

 

[ma55ter_fett]

The birth of each is an independent event. For simplicity's sake, it's the same as flipping a coin, and we're being asked the chance that we're getting two of a kind. 50% per result for each of 2 results = .5 * .5 = 25% chance that the results will be the same.

I think that this question is open to two different interpretations

1st interpretation) What is the chance of having two male children, to which the answer is 25% as you pointed out.


2nd interpretation) A woman has one child who is male, she then has a second child, what is the chance that the second child is male? To which the answer would be 50/50.

I'm thinking it was the second myself, though I am not quite sure.