"The king comes from a family with 2 children. What is the probability that his sibling is his sister?"

is it that easy? .5?
or am i missing something.

9/11/2007 9:40:07 PM

looks like 50/50 to me, but im no statistician

[Edited on September 11, 2007 at 9:55 PM. Reason : 0]

9/11/2007 9:55:26 PM

do you really have a question worded exactly that way?

9/11/2007 10:07:56 PM

could be a trick question...if the question was worded "what is the probability that his sibling is A sister" then it would definitely be 50/50, but with its wording it looks to me that the answer is 100% chance, since he came from a family of 2 children and he evidently has a sister ("chance his sibling is HIS sister")

[Edited on September 11, 2007 at 10:39 PM. Reason : to make it easier to understand, hopefully]

9/11/2007 10:38:06 PM

2/3

[Edited on September 11, 2007 at 10:45 PM. Reason : ]

9/11/2007 10:44:56 PM

the question is exactly how it is above. i see the 100% view, but feel like the question isnt saying that is his sister, rather just asking for that possibility???

9/11/2007 10:45:36 PM

What class is this?

9/11/2007 10:58:27 PM

ST 421, prob the easiest follow up to any stat classes.

9/11/2007 11:03:51 PM

found essentially the same question on another site and now i got it down between .5 and 2/3.

50% seems like the obvious answer b/c probability you have a boy vs. girl =.5

2/3: (This is some of their reasoning)

All possible 2 sibling families: BB, BG, GB, GG.

GG is eliminated b/c you know you have a boy. So now your possibilities are BB, BG, or GB. 2/3 of those have a G (sister).

Makes sense, but so does 1/2..kinda leaning to 2/3 now :-/

9/11/2007 11:20:00 PM

^aren't BG and GB the same thing? You are back to 1/2

9/11/2007 11:45:02 PM

^essentially they are the same thing, but .5/(.25+.5) when omitted the GG (.25) is .5/.75 = 2/3




Same reason that the sample space for flipping a coin twice is {HH, HT, TH, TT}

[Edited on September 12, 2007 at 12:14 AM. Reason : g]

9/11/2007 11:57:15 PM

nevermind.. search internet for "Jeremy comes from a family with 2 children"

google got me through 75% of my computer science degree

[Edited on September 12, 2007 at 12:08 AM. Reason : sfsaf]

9/12/2007 12:02:55 AM

i dont think that that is the point it is getting at though. you KNOW the king is male. he can have a younger brother, older sister, or younger sister. 2/3.

[Edited on September 12, 2007 at 12:08 AM. Reason : rntk]

9/12/2007 12:04:57 AM

check this ^^

9/12/2007 12:09:56 AM

yeah just looked it over, along the same lines as the other site i found. it is a dumb question though to begin with though.

9/12/2007 12:12:51 AM

Quote :

"2/3: (This is some of their reasoning) All possible 2 sibling families: BB, BG, GB, GG. GG is eliminated b/c you know you have a boy. So now your possibilities are BB, BG, or GB. 2/3 of those have a G (sister)."

That is poor reasoning. That's like saying the roulette table just came up black ten times in a row, so there's a 99% chance the next spin will be red.

I used the logic stated several posts below when I listed my answer.

Quote :

"he can have a younger brother, older sister, or younger sister. 2/3."

9/12/2007 8:34:32 AM

Quote :

"found essentially the same question on another site and now i got it down between .5 and 2/3. 50% seems like the obvious answer b/c probability you have a boy vs. girl =.5 2/3: (This is some of their reasoning) All possible 2 sibling families: BB, BG, GB, GG. GG is eliminated b/c you know you have a boy. So now your possibilities are BB, BG, or GB. 2/3 of those have a G (sister). Makes sense, but so does 1/2..kinda leaning to 2/3 now :-/"

It's 50%. You have to remember you have condition probability here. Given the first child is a boy, what's the probability the second is a girl. So essentially GG isn't an option. Also the BG GB and BB looks at BG and GB to be different. But in the context of your question, they're the same.

Also I don't know if you learned the binomial distribution, but you can do

2 choose 1 * (.5)*(.5) = .5

[Edited on September 12, 2007 at 9:17 AM. Reason : ]

9/12/2007 9:06:36 AM

So, basically you are saying there are two possibility BB and BG/GB. What if you break that down into more specific scenarios. BoyKing KingBoy KingGirl GirlKing. The first scenario could not occur since the second boy would not be king. That leaves a 33% chance the King was born first followed by a boy, a 33% chance the King was born first followed by a girl, and a 33% chance the King was born second preceded by a girl.

9/12/2007 9:19:33 AM

going with the topics we've been doing in class, using P(A|B)...P(A n B)...etc, I feel like .5 isnt using what we have learned and makes more sense to use it, getting 2/3.


--just relate it to flipping a coin. calling Tail = boy, Head = girl. You would assume that if you tossed it 100 times, you would have 25 TT, 25 TH, 25 HT, 25 HH. But you know you already have one boy. So using the GIVEN info, the useful information is now, 25 TT, 25 TH, 25 HT. So you have 25 out of 75 (1/3) chance the other coin (sibling) was also a tail (boy) while 50 out of 75 were heads (girls), thus 2/3.

[Edited on September 12, 2007 at 10:06 AM. Reason : o]

9/12/2007 10:02:10 AM

its P(G l B)=P(G n B)/P(B)

9/12/2007 10:26:51 AM

P(G | B) = P( B n G)/ P(B) = (.5*.5)/(.5) = .25/.5 = .5

9/12/2007 2:46:37 PM

ye old conditional probabilities, making easy questions hard by ambiguous wording, woo hoo.

9/12/2007 3:53:57 PM

50%

9/12/2007 4:04:08 PM

The "king" aspect is the only thing that makes this problem ambiguous for me.

Some people seem to be assuming the king (or queen) is the first born. I'm not sure that is intended by the problem. In that case, however, there are only two possibilities (given that we have a king instead of a queen):

Boy first, then girl

Boy first, then another boy.

With this assumption, the answer is 50%.

On the other hand, if the king is just one of the two children (regardless of birth order), it's different. We know one is a boy, so we have three equally likely possibilities:

Boy first, then girl

Girl first, then boy

Both boys

In that case, the probability the king's sibling is a sister is 2/3.

9/12/2007 4:15:46 PM

so what's the answer?

9/12/2007 4:16:06 PM

I just gave you the answer. I didn't write the problem. I don't know if "king" is meant to imply first born. I say it shouldn't--the oldest can always abdicate. I'd go with 2/3.

9/12/2007 4:19:23 PM

Quote :

"he can have a younger brother, older sister, or younger sister. 2/3."

what does AGE have to do with ANYTHING? all you did was split the female gender of sibling into two different catagories, then unfairly weighing it instead of breaking it down like this:

odds of younger bro: 0.5
odds of older sis: 0.25 (of 0.50)
odds of younger sis: 0.25 (of 0.50)

you can't assume order meaning anything because it doesn't say his age relative to the other sibling.

this question is only asking if the SIBLING OF THE KING is MALE or FEMALE

this question is NOT asking whether the gender distribution of the family (as a whole) of the PARENTS OF THE KING is BG, GG, or BB

this is why you can't view it like this:
G then B
G then G
B then G
B then B

because this is looking at TWO people instead of one (both siblings).

this is where you people are getting tripped up.

if I have a long lost sibling and I have no other information available on the gender of that sibling, I'm going to assume there's an equal chance that my sibling is either my brother or my sister. REGARDLESS of MY gender, the chance remains EQUAL. IGNORE the parents past production because it has no implication on their future production.

p = .5

I think this is just a simple test of logic, because people want to view the family as a whole instead of the irrefutable fact that the gender of any unknown person is 50/50.

OF COURSE if we are to assume the KING was always born first it STILL doesn't matter because once he is born, the odds of the royal family's next child will STILL be 50/50. Ignore the King's gender!

[Edited on September 12, 2007 at 5:02 PM. Reason : .]

9/12/2007 4:34:37 PM

you eventually ignore the kings gender in this case because the gender of the first and second child are independant variables but to be technically correct you still have to acknowledge it as a conditional probability and no age doesn't mean anything.

9/12/2007 5:12:25 PM

is it supposed to mean something that he's a KING or not?

I don't think so

assuming we have a king, and he has a long lost sibling, why would it matter when the other child was born in terms of gender? WHEN that child was born it had an equal chance of being male and female

I guess my point is that we know no circumstances that would change this chance that were stated in the original question.

[Edited on September 12, 2007 at 5:34 PM. Reason : .]

9/12/2007 5:22:13 PM

The determination of sex is independent from one child to the next. Thus, p = 0.5

9/12/2007 6:27:46 PM

1/2 or 50% - has to be

there are 2 children - the king is either the first or second - but the sibling can be a boy or girl so 50/50 chance

9/12/2007 6:32:21 PM

I looked it up, it's 2/3,

9/12/2007 7:15:03 PM

NNNNNNN


CCCCCCC


STATE

N-C-STATE

9/12/2007 8:41:09 PM

i know that the individual probability of having just 1 boy or girl is .5. but again, same with flipping a coin. go flip yourself a coin a whole bunch of times and write down your 2 flip combinations. call Tails for boy and Heads for girl. Eliminate all the HH or girl girl combos, then given that you have a boy already (tails), count up the number of heads left (girls) and divide it over the total number of boys and girls you had left. (# of Heads)/(# of Heads + # of Tails) = about 2/3. There is your real life example.

9/12/2007 9:42:05 PM

^you're counting two kids ("combos"), not one. assuming each coin represents a child in the family, if you want to flip two coins, fine, but one of the coins has to be tails 100% of the time because we already know it's a boy. so there's no fucking point flipping that coin, is there?

so we're left flipping one coin with two sides. EQUAL PROBABILITY.

the question asks if his sibling (1 person) is his sister (a girl). the odds of one person being a girl is 50%. so you flip the only coin in question..

[Edited on September 12, 2007 at 10:26 PM. Reason : .]

9/12/2007 10:21:04 PM

what if she is a tranny?

9/12/2007 10:45:17 PM

^^

How do you know which coin to flip and which one not to flip? Both of them have the potential to be tails.

9/12/2007 10:50:21 PM

the plane will not take off

9/12/2007 10:50:44 PM

^^^^ there are two correct answers.

The probability that a child in a family with two children is a boy with a sibling sister is 2/3.

The probability that a new sibling is a girl is 1/2.

It depends on if you wish to view the system as a whole or just as the moment in time where the boy is already born (and hence we know he is a boy).

This stupid discussion is much like the one where people poo poo folks who say something like "wow that family has 6 boys in a row I doubt the next one will be a boy". Are the people who make such comments talking just about the next child about to born ? No of course not, that's not interesting. What's interesting is the family as a whole which would have 7 boys. Technically of course, once you know the last 6 are boys there is no question of probablity, those things are certain, and there is a 50/50 chance on the next kid. But, people do not speak in terms of pedantic technical probabilities.


[Edited on September 12, 2007 at 10:52 PM. Reason : can't count.]

9/12/2007 10:50:45 PM

IMO- If the question wanted order to matter, age/birth order would have been mentioned.

Who knows what Gerig actually expected, though. I'm in 421 with him this semester, too.

9/12/2007 11:01:43 PM

Quote :

"^^^^ there are two correct answers. The probability that a child in a family with two children is a boy with a sibling sister is 2/3. The probability that a new sibling is a girl is 1/2."

yes, and given the wording of the question I can only assume that the latter is correct, because it's coming from a singular (his sibling) rather than a group (family) point of view. this is the classic anti monty hall case.

9/13/2007 12:07:57 AM

who says the king is one of the children?

9/13/2007 12:23:41 AM

the plane will not take off

9/13/2007 12:47:49 AM

The answer is 1/2.

The trick of the questions is two assume that: bb gg bg gb :are the four combinations. The WRONG thing to do would be to assume that one of them is out of the running for because the King is one of those. For the other sibling is just as likely to have the kings makeup as they do another.

People do this all the time. They think that if they have been losing at poker all night their chances are better since theyve been losing so much. Every hand has the same probability to start with. They dont change because you have been losing

9/13/2007 2:02:15 AM

50%

here's another way to look at it.

the children in the family are one of four combinations: BB BG GB GG

if King (a boy) is the first sibling (B), there are two possibilities: BB or BG. 50% chance his sibling is G.

if King is the second sibling (B), there are two possibilities: BB or GB. still a 50% chance his sibling is G.




[Edited on September 13, 2007 at 2:59 AM. Reason : ]

9/13/2007 2:55:05 AM

someone posted this on the class forum and this is the teachers response of help:


"Here it is all a matter of getting the sample space written correctly. Then count how many outcomes correspond to the event that the King has a sister."

Judging by that, I'd assume he is looking for the 2/3 answer.

9/13/2007 10:20:49 AM

sounds like the teacher didn't word the question very well, then
probably in attempt to avoid google searching the answer

9/13/2007 10:37:52 AM

i dont care what the "teacher" says, my answer ^^^ is correct.

9/13/2007 10:57:58 AM

^assuming that the knowledge that the "King" is a boy is certain. Not an unreasonable assumption in this case.

9/13/2007 11:30:42 AM

^^ You assume that the age of the king is known. It's not. Which is why you have to count both the possibilities BG and GB. 2/3 is the right answer since whether the king is the older or younger sibling isn't specified.

9/13/2007 12:39:05 PM