Current Events > Suppose a couple has 3 kids and at least one is a girl...

(+) Yeah! (+)

What's the probability all three kids are girls?

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Whatever the parents want, because all 3 kids are adopted.
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trick question they're all robots
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50%. Either they are all girls or they aren't.
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And that girl was Albert Einstein
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24.15% according to birthrate statistics.

Marginally more likely that they would both be boys.
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I hate that i forget how to calculate this.
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is it 0.25?

There are four possible outcomes for the other two kids:
1: boy, boy
2: boy, girl
3: girl, boy
4: girl, girl

1/4, or .25%.

UnfairRepresent posted...

24.15% according to birthrate statistics.

Marginally more likely that they would both be boys.

Huh. I thought I read/heard that baby girls have a slightly better survivability than baby boys.
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1/7

Also:


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how about this.

a couple has 3 kids, and 1 is a girl. what is the probability that they have 2 or more girls?
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yes its 1/7

ChromaticAngel posted...

how about this.

a couple has 3 kids, and 1 is a girl. what is the probability that they have 2 or more girls?

4/7
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1. why are there so many different answers to this question

2. what is the explanation for the 1/7 answer

3. In Laserion's solution, how are boy/girl and girl/boy both counted as separate outcomes
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randy_123r posted...

DuranOfForcena posted...

ChromaticAngel posted...

how about this.

a couple has 3 kids, and 1 is a girl. what is the probability that they have 2 or more girls?

if Laserion's solution is correct, and i think it is, then it would be 75%

Yep. The probability of having 2 or more girls is the same as the 1 minus probability of having the rest of them being boys. Which is 0.75 or 75 %

nah, the first poster got it right with 4/7

BBB - 0 probability, ignored.
GBB - fail
BGB - fail
BBG - fail
GGB - success
GBG - success
BGG - success
GGG - success

4/7
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boys are more likely

which early research suggest that since the y chromosome is smaller than the x and may swim faster

but nothing concrete
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Supra574 posted...

boys are more likely

which early research suggest that since the y chromosome is smaller than the x and may swim faster

but nothing concrete

I heard studies a long time ago suggesting that the more sex a man is engaged in, it increases the chances of having a girl. the longer he goes without sex, it increases the chances of a boy.
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ChromaticAngel posted...

I heard studies a long time ago suggesting that the more sex a man is engaged in, it increases the chances of having a girl. the longer he goes without sex, it increases the chances of a boy.

i've heard of this but I say it's far-fetched for two reasons

it's hard to even test this let alone make a claim
and
I'm pretty sure the production of gametes are completely random and not at all consistent between people because diversity leads to a stronger species overall

but if there have been tests on gamete diversity please let me know (no sarcasm)
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Supra574 posted...

ChromaticAngel posted...

I heard studies a long time ago suggesting that the more sex a man is engaged in, it increases the chances of having a girl. the longer he goes without sex, it increases the chances of a boy.

i've heard of this but I say it's far-fetched for two reasons

it's hard to even test this let alone make a claim
and
I'm pretty sure the production of gametes are completely random and not at all consistent between people because diversity leads to a stronger species overall

but if there have been tests on gamete diversity please let me know (no sarcasm)

this was a long time ago, I doubt I'd be able to find the articles again if I tried. Plus just because something happened in a study doesn't mean it's a law of nature.
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ChromaticAngel posted...

this was a long time ago, I doubt I'd be able to find the articles again if I tried. Plus just because something happened in a study doesn't mean it's a law of nature.

oh I'm not stating that at all. Apologies if that was the impression. I'm just a skeptic by nature (no pun intended)
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Talks posted...

1. why are there so many different answers to this question

Because calculating probabilities can rapidly become very tricky.

2. what is the explanation for the 1/7 answer

If we know nothing except there are three children, and we assume that boys and girls are equally likely to occur, then there are 8 total cases with equal probability. Note that we take into account the order in which the children were born.

BBB
BBG
BGB
GBB
BGG
GBG
GGB
GGG

In this case, we can readily see that the odds of three girls are 1/8. However, we know more than that. We know that there are three children, and that one of those children is a girl. Therefore the first case--BBB--can't have occurred. All of the other cases are still equally likely. That leaves 7 possibilities, 1 of which is GGG, so the odds are 1/7.

Note that if we knew that first child was a girl, then the odds would be rather different. In this cases, the odds of GGG would be 1/4. The same is true if we know that the second child is a girl, or if we know the third child is a girl (in each case, the specific information rules out four of the eight possibilities).

3. In Laserion's solution, how are boy/girl and girl/boy both counted as separate outcomes

Because it's a convenient way to list outcomes with equal probability. We could instead count only three cases: BB, BG, GG, but if we did that then we would also have to note that BG was twice as likely to occur as BB or GG.

The easiest way to solve this is to just list the 8 cases, eliminate the one with no girls, and trivially note that one of the remaining seven has all three being girls, so the answer is 1/7, working with the assumption that boys are girls are equally likely outcomes, of course.

Another way is to use the conditional probability formula: The probability of event B occurring given that event A has occured is equal to the probability of the intersection of A and B divided by the probability of A.

Let A be the event that there is at least one girl and B be the event that all three children are girls. P(A) = 7/8, P(A intersect B) = P(B) (as any outcome with three girls clearly has at least one girl) = 1/8, and (1/8) / (7/8) = 1/7.
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Laserion posted...

There are four possible outcomes for the other two kids:
1: boy, boy
2: boy, girl
3: girl, boy
4: girl, girl

This is stupid. Boy girl is the same as girl boy and shouldn't be calculated separately
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Howl posted...

This is stupid. Boy girl is the same as girl boy and shouldn't be calculated separately

That's fine as long as you take into account that Boy-Girl is twice as likely as Boy-Boy (and similarly, twice as likely as Girl-Girl).

Howl posted...

This is stupid. Boy girl is the same as girl boy and shouldn't be calculated separately

no. each child independently has their own chance to be a boy or a girl.

Like, if you flip a coin 100 times, you're probably going to get close to 50 heads and 50 tails.

You don't give 100 heads the same probability weight as you do to some mix of heads / tails.

the same principle applies even if you only flip 2 coins, or in this case 2 kids.
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Is there one answer everybody can agree on? I'm not good with this kind of word problem but I want to know.
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tiornys posted...

Talks posted...

1. why are there so many different answers to this question

Because calculating probabilities can rapidly become very tricky.

2. what is the explanation for the 1/7 answer

If we know nothing except there are three children, and we assume that boys and girls are equally likely to occur, then there are 8 total cases with equal probability. Note that we take into account the order in which the children were born.

BBB
BBG
BGB
GBB
BGG
GBG
GGB
GGG

In this case, we can readily see that the odds of three girls are 1/8. However, we know more than that. We know that there are three children, and that one of those children is a girl. Therefore the first case--BBB--can't have occurred. All of the other cases are still equally likely. That leaves 7 possibilities, 1 of which is GGG, so the odds are 1/7.

Note that if we knew that first child was a girl, then the odds would be rather different. In this cases, the odds of GGG would be 1/4. The same is true if we know that the second child is a girl, or if we know the third child is a girl (in each case, the specific information rules out four of the eight possibilities).

3. In Laserion's solution, how are boy/girl and girl/boy both counted as separate outcomes

Because it's a convenient way to list outcomes with equal probability. We could instead count only three cases: BB, BG, GG, but if we did that then we would also have to note that BG was twice as likely to occur as BB or GG.

the_rowan posted...

The easiest way to solve this is to just list the 8 cases, eliminate the one with no girls, and trivially note that one of the remaining seven has all three being girls, so the answer is 1/7, working with the assumption that boys are girls are equally likely outcomes, of course.

Another way is to use the conditional probability formula: The probability of event B occurring given that event A has occured is equal to the probability of the intersection of A and B divided by the probability of A.

Let A be the event that there is at least one girl and B be the event that all three children are girls. P(A) = 7/8, P(A intersect B) = P(B) (as any outcome with three girls clearly has at least one girl) = 1/8, and (1/8) / (7/8) = 1/7.

Are these jokes to confuse people? The answer is obviously 25%.
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ConfessPlease posted...

Are these jokes to confuse people? The answer is obviously 25%.

What's your reasoning?

tiornys posted...

ConfessPlease posted...

Are these jokes to confuse people? The answer is obviously 25%.

What's your reasoning?

"If I don't say something like this, the topic won't get to 500."

That's the reasoning.
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reeekt posted...

Is there one answer everybody can agree on? I'm not good with this kind of word problem but I want to know.

it's 1/7 (post 27 explains why). CE is notoriously bad at probability, plus add in all the meme answers...
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DuranOfForcena posted...

reeekt posted...

Is there one answer everybody can agree on? I'm not good with this kind of word problem but I want to know.

yeah i think Laserion was wrong now, 1/7 is the correct answer

the most obvious answer is 1/3, and i thought that Laserion's was correct because it brings up the fact that a girl/boy situation is different from a boy/girl situation in this case, thus 1/4 not 1/3, but now i see that that being true also means that it shouldn't be assumed that the first child is a girl in all cases. so, 1/7.

This is incorrect. You aren't determining the probability that all the children are girls because one of them is guaranteed to be a girl. It's like flipping three coins but one of those coins only has heads.

1/4 is objectively the correct answer.

Another way to phrase this question is what is the probability of getting 2 heads on 2 coin flips and flipping a third coin that only has heads.
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Howl posted...

This is incorrect. You aren't determining the probability that all the children are girls because one of them is guaranteed to be a girl. It's like flipping three coins but one of those coins only has heads.

but you don't know which one, so you still need to look at all three.

edit: misread. no. one coin is not heads/heads. it's a regular coin that you know the result of already. not the same thing.
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Howl posted...

This is incorrect. You aren't determining the probability that all the children are girls because one of them is guaranteed to be a girl. It's like flipping three coins but one of those coins only has heads.

No, to get that scenario you'd have to know which child was a girl. You don't know that--you only know that one of them is a girl.

tiornys posted...

Howl posted...

This is incorrect. You aren't determining the probability that all the children are girls because one of them is guaranteed to be a girl. It's like flipping three coins but one of those coins only has heads.

No, to get that scenario you'd have to know which child was a girl. You don't know that--you only know that one of them is a girl.

What you know is irrelevant because 1 of them has a 100% chance of being a girl and has a 0% chance of being a boy.
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Howl posted...

What you know is irrelevant because 1 of them has a 100% chance of being a girl and has a 0% chance of being a boy.

Which one?

To be clear, if you're drawing an analogy to coin flipping, then swapping out a coin is the same as choosing a specific child to be a girl.

tiornys posted...

Howl posted...

What you know is irrelevant because 1 of them has a 100% chance of being a girl and has a 0% chance of being a boy.

Which one?

It's irrelevant one of the coins only has a heads side so you don't have to factor the probability that any particular coin has that. The only 4 possible outcomes are always going to be

HHH
HTH
HTT
HHT

Or in this case with boys and girls

GGG
GBG
GBB
GGB
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NO. read the question again. one of the coins is H, but not necessarily the first one. TTH is a valid positive result, and it different than HTT or THT.
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Medussa posted...

NO. read the question again. one of the coins is H, but not necessarily the first one. TTH is a valid positive result, and it different than HTT or THT.

No it isn't. One of those two will always occur with 100% certainty so they are effectively exactly the same result.
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Howl posted...

It's irrelevant one of the coins only has a heads side so you don't have to factor the probability that any particular coin has that. The only 4 possible outcomes are always going to be

HHH
HTH
HTT
HHT

Yes, this is true if you replace a coin. But replacing a coin is not properly analogous to the problem. As noted in my edit, when you replace a coin you're selecting a specific child to be a girl, and that creates a greater constraint on the probabilities than is justified by the information given.

Manocheese posted...

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Howl posted...

Medussa posted...

NO. read the question again. one of the coins is H, but not necessarily the first one. TTH is a valid positive result, and it different than HTT or THT.

No it isn't. One of those two will always occur with 100% certainty so they are effectively exactly the same result.

no, it's not. read post 27.

edit: go back to the original framing. how is the oldest child being a girl the same result as the middle child being a girl?
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Medussa posted...

Howl posted...

Medussa posted...

NO. read the question again. one of the coins is H, but not necessarily the first one. TTH is a valid positive result, and it different than HTT or THT.

No it isn't. One of those two will always occur with 100% certainty so they are effectively exactly the same result.

no, it's not. read post 27.

I did read it, and it's incorrect
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Howl posted...

I did read it, and it's incorrect

What makes it incorrect?