Uncle Scrooge
Uncle Scrooge have three children, Huey, Dewey, and Louie. If atleast one of them is a girl,
What is the probability that all children are girls?
What is the probability that all children are girls?
Labels: mathemagic, thinktank
posted by Rajesh Lal at
8:35 AM
63 Comments:
I believe Duck Tales pretty clearly demonstrates the nephews are boys as they all three wear baseball caps - a garment which, were a girl to wear it - would cause Disney Reality Child Services to take the girl away and place her with a more family values-respecting foster parent, such as Goofy or possibly Darkwing Duck.
Duck Tales? Was unaware of relevence of characters' names. I just stuck to the maths side of it. 1 of the 3 is definitely a girl (irrelevant which one) , leaving 2 others of undetermined gendre. Chances of both being girls is 1/2 x 1/2 = 1/4. correct me if i'm wrong please as i feel there should be more to it than that!
*gender
Since I could never quite wrap my head around probability in high school, I'm probably doing this wrong (or at least inefficiently), but...
Since it is given already that one of the kids is a girl, the real odds we're looking for are that the other two are as well. So:
Scenario 1 - HDL2:Boy ; HDL3:Boy
Scenario 2 - HDL2:Boy ; HDL3:Girl
Scenario 3 - HDL2:Girl ; HDL3:Boy
Scenario 4 - HDL2:Girl ; HDL3:Girl
So I'm going to say the odds are 1/4.
Well, my guess will have to be 1/4, since if one of the kids is a girl, then there will be:
G B B
G B G
G G B
G G G
I just think that the odds being 1/4 isn't a very hard think to figure out, but i can't imagine anything that could make it be different
that is too good to be true
pete thats why the question says "IF"
They have 3 kids. One is a girl - at least. So, these are the combinations...
Girls Boys
1 2
2 1
3 0
Therefore, there are 3 combinations, and if only 1 of the combinations contains 3 girls, then wouldn't the answer b 1/3 chance of all 3 children being girls?
Correct me if I'm wrong.
I think the answer should be 1/7 !
There are 8 possibilities for the pattern of gender - bbb,bbg,bgb,bgg,gbb,gbg,ggb,ggg
we know that bbb is not the case so that leave 1/7.
let me know if you disagree
bald got it before me. i agree, 1/7, all the others is wrong.
Pete "I believe Duck Tales pretty clearly demonstrates the nephews are boys "
Nephews are (implied) boys, its niece who are girls :)
wow guys, it's really not that hard!
if only one of them is a girl, there are 3 different possible combinations that could occur.
if two of them are girls, then there are three more combinations that could occur.
and there is only one possible combination that they're all girls.
So, taking all of the possible combinations between 1 and 3 girls. Only one of them will net you 3 girls.
So the probability will be 1/(3+3+1)
which is equal to...
1/7
umm if it is uncle scrooge how the f does he have children, and if he's an uncle to them how are they his children
the answer is 0. Uncle Scrooge does not have any children. Huey,Dewey, and Louie are his nephew. If at least one of them is a girl, it won't matter because the girl would not be his daughter.
It is irrelevant as to which is a girl.
Any combination of one girl and two boys is the same whether is be GBB, BGB, or BBG. Any of those is already represented by the statement.
The remaining variances include GGB or GGG. Since there is already a GBB combination, the answer should be 1/3 or 33% chance that all are girls.
To wit-
GBB 1/3
GGB 1/3
GGG 1/3
There is 2/3 chance that the others are boys.
Bald, in your entry, you gave 8 possibilities. "bbb,bbg,bgb,bgg,gbb,gbg,ggb,ggg
" the first is out ,, yes but the second,third, fifth are all the same, and the fourth, sixth, and seventh are the same , then there is the last one, so only 3 real possibilities. so 1/3 is the real answer using your logic which seems reasonable to me,, Johnr
bald n yujin, you are both WRONG.
your pattern of "bbb,bbg,bgb,bgg,gbb,gbg,ggb,ggg" is wrong.
the question did not mention which gender came first. in other words, the position of G(s)d B(s) does not matter.
therefre, the CORRECT pattern would be "GBB,GGB,GGG" or any patterns that shows:
1st case: at least 1 girl
2nd case: at least 1 girl, so 2 girls are also accepted
3rd case: at least 1 girl, all of them are girls are also accepted.
So, for the probability of getting all girls is 1/3.
Hey Eric, the question does not say that the children are his children.
Rather it says, "what is the probability that all children are girls?"
ruriko you are wrong.
Position does matter...
H D L
G B B
G G B
G B G
G G G All Girls
B G B
B B G
B G G
So 1/7 is right.
Your pattern does not account for the fact that while Huey and Duey could be Boy that Luey is Girl or Huey and Luey are Boy and Duey is a Girl
-Ashley-
AShley.. I'm sorry to say this but YOU are WRONG.
Position DOES matter.
Position is this case refers to which child comes first. Or rather which gender comes first. Lets say Scrooge has kid, and the 1st one is a girl, and the 2nd n 3rd are boys. It wont matter because he still has a girl no matter if his daughter is the 2nd or 3rd child. Now do you understand my point?
The names Huey, Dewey and Louie do not depict the fact that Huey came 1st or Louie came last or vice versa.
Oh.. Now i see your point
-Ashley-
(-.-') didn't expect an express reply...
I would also agree to the answer "0" because Uncle Scrooge is an uncle. And Disney did not give him any children of his own.
1/7
Your not taking into account the fact that the girl can switch. You need to take into account that Huey Duey and Louie can each be a girl 4 times and a boy 3.
So I feel 1/7 is right.
Knowing that atleast 1 of the children is a girl SHOULD NOT change the probability.
SO, it should be 1/8.
Ydrameos, imagine if you had a chance to with the lottery if you could guess the correct three letter combination of b's and g's. For instance you could guess bgg or bgb or bbb. Do you really think that your odds of winning wouldnt go up if you knew that the winning combination wasn't bbb?
3g- ggg
2g 1b - ggb gbg bgg
1b 2g - gbb bgb bbg
bbb is eliminated because one is a female
1/3 Is the answer
2/2 x 1/2 x 1/2 = 2/6 = 1/3 :)
... I just think it's interesting that the answer is in such contention. That fact should probably signify a clarification of the problem.
I personally thought it was 1 in 4, but hey, that's just me.
.875
or
7/8
If you us a the probability function on a scientific calculator.
n=3 p=.5 k=1,2,3
i know i just finished a unit on this in pure math
Let me put it this way:
3 Children (1st, 2nd and 3rd)
-Probability that 1st child is girl = 1/2.
(because we are looking for the probability of all girl, 1st child = girl; thus we satisfied the atleast 1 girl criteria).
-Probability that 2nd child is girl = 1/2.(1st child = girl)
-Probability that 3rd child is girl = 1/2.(1st & 2nd = girl)
i never realised how hostile a simple answer to a question could get.....order does not matter in determining sex of a child...for every birth there is a 50% chance of boy and 50% chance of girl....the only thing that matters is the combinations of boys and girls
so....
1 girl, 2 boys
2 girls, 1 boy
3 girls, no boys
therefore 1/3 or 33% chance of being all girls.....names are irrelevant...however, i agree that uncle donald cannot have children...and the girl in duck tails was not named huey, duey, or luey.....nor do names reflect gender in todays day and age
As one is definately a girl, we need only calculate the possibilty of having 2 girls from 2 children. For each child the possibility is 50% of being female or 0.5 probability. To have 2 girls you multiply the possibilities of 0.5. Therefore 0.5 x 0.5 = 0.25 or 25% or 1/4.
The question is what is the probability that ALL children are girls? It does not say the probability of the three children being girls, therefore the answer is 0 unless all the children on the planet are girls.
It is 1/8. When talking about probability one must consider ALL possibilities. In this instance there are 8 possibilities:
BBB
BBG
BGB
GBB
GGB
GBG
BGG
GGG
The question asks about all girls, since there is only one GGG and 8 possibilities it is 1/8.
An easier way to solve this is by doing it like this:
H 50%B 50%G
D 50%B 50%G
L 50%B 50%G
so prob of HDL all being G is
(1/2)(1/2)(1/2) = 1/8
Do you have to consider all possibilities when we know that one of the children is a girl?
One of them is a girl...You are only determining the probability that the other 2 children will be girls
bb gb gg
so the answer is 1/3....as i said before
Okay guys... and girls. IT'S 1/7.
Position DOES matter and there is a reason why there are names!
Since we know that at least one of them is a girl, then there are three different possible combinations that there is only one girl within the 3 kids!
For the more mathematically inclined, this is 3 pick 1 instead of 3 choose 1.
For example, if we were given that question and it asked "what were the chances that (blank) is the girl?" We would say: there is 1/3 chance that (blank) is the girl. Because there could be two situations where either of the other two kids was the girl.
Therefore we have the following SO FAR:
BBG
BGB
GBB
Representing the different children.
Then there's the possibility that TWO of the kids are girls. Again ORDER COUNTS! Using the same situation above, we will have:
BGG
GBG
GGB
And finally, if they were all girls, there is only one possible combination!
GGG
So if you add that all up, there are 7 possible gender orientations of the children (barring transexuality) and only of those possibilities yields all girls!
It is NOT 1/8 because BBB IS NOT a possibility since the question explicitly states that there is AT LEAST ONE GIRL.
Furthermore, they are not HIS kids. The point of the question is to answer the question, not to be stupid and try to say that the question has no base and therefore has no answer.
Someone can be called Uncle even if they're not actually an uncle to someone, and maybe to you he is your UNCLE, but to those kids, he is the FATHER. Who's to say what perspective this question is in?
This is all semantics that is REALLY UNIMPORTANT. If you don't know the answer, don't try to discredit the question <_<.
QED.
Sorry my bad it should actually be 1 choose 3 not 1 pick 3. Got them mixed up.
Scrooge is their great-uncle; Donald is their uncle.
QED
well~~ answer is 1/7
if it's a math question
otherwise
it's undefined
done
lol
Everyone who said the possibility is anything but 1/3 is a moron.(this is not including word play or any factors of what disney said)
position DOES NOT matter.
if you're a girl and you had two siblings, what are the chances they are both girls? the answer is regardless of whether they're older than you or younger than you.
guys who said 1/8 are complete idiots
1/7 isn't much better
dude who just finished a course in pure math needs to retake that class again cause you should have failed
1/4
point three,
the question is not asking if you are the girl, what are the chances that the other two would be girls as well.
Position does matter because different people can be different genders. And age has nothing to do with this either.
I really don't know how to explain this any better other than, "you're an idiot". I don't want to resort to name calling but the idiocy and frustration of the comments on this page is seriously ticking me off.
The answer to this question can be found using some "higher level math"
3 choose 1 + 3 choose 2 + 3 choose 3. You cannot dispute that this is the correct equation, and this will get you 1/7.
3nCr1+3nCr2+3nCr3=7
For goodness sake, the answer is 1/7.
To simplify the question 1st, lets take out the "at least 1 is a girl".
We will have
1/2 x 1/2 x 1/2 = 1/8
so there is only 1 out of 8 combinations that 3 children is a girl.
if we consider the fact that at least 1 is a girl, that will leave us with only 7 combinations.
So the chance of getting 3 girls with at least 1 being a girl is 1/7.
For goodness sake, everyone just defends their own answer, but never explains the mistake in the other.
The problem with 1/3 is that it assummes that 1Girl 2Boys, 2G 1B, and 3G 0B are EQUALLY LIKELY. This is NOT true. It is more likely to get 1G 2B (or 2G 1B) than it is to get 3G 0B. Why? because 1G 2B could be gbb, bgb, or bbg, while 3G 0B can only happen when you have ggg.
Whats more likely when you flip a coin three times, 1 head and 2 tails, or 3 heads?
When finding probability, placing the number of possibilities that work in the numerator, and the total possibilities in the denominator only work when every possibility is EQUALLY LIKELY.
So, 1/7 works because the seven listed possiblities are all equally likely. They each have a 1/8 chance of occuring (.5^3).
Instead of calling people idiots, try to show WHY they are wrong (not just why you are right) so they have a chance to correct their thinking.
it's simple probability of independent events, so first off, forget the combinations.
We already know one is a girl, so the other 2 children have 1/2 chance of being either boy or girl.
Therefore, you multiply the probability of 2 independent events, and, voila, 1/2 * 1/2 = 1/4
Is not aerospace engineering (rocket science)
-If they are TRIPLET (thus, Single event,like flipping 3 coins at the same time), probability = 1/7.
-If NOT, thus 3 independent event (like fipping 1 coin, 3X), probability = 1/8.
-If we know that Huey=Girl .or. Dewey=Girl .or Louie=Girl, probability = 1/4. (one event is taken out of the equation because we already know its outcome).
NOTE: Knowing atleat 1 is Girl, we canNOT say for sure that Huey=Girl or Dewey=Girl or Louie=Girl'
ok upon further thought, my answer changes to 1/4
reasoning:
the question is as if there are 3 fair coins one of which is already heads. now what are the chances the other two will be heads? they're independent of each other. the first one has a 1/2 chance and same with the second. therefore 1/4
i'd like to thank jeditony for sparking the change in my thought, may the force be with you
hello????
anyone listen in maths at school??? its 1 in 4
1 in 2 chance of a child being of a certain gender and we are only speculating on the gender of 2 children so its 1/2 x 1/2 = 1/4!!!!
however i do agree its a trick question
hi read the question again! it only asks what is the chance of any child being a girl.... its 1 in 2....
the answer is 1/2 guys
wow such controversy. I'm sorry i've missed all the excitement.
first child is born.
prob boy = 1/2 prob girl = 1/2
second child is born.
prob boy = 1/2 prob girl = 1/2
third child is born.
prob boy = 1/2 prob girl= 1/2
probability all girls = 1/2x1/2x1/2
= 1/8
HOWEVER
the fact that there is at least one girl is a GIVEN and THEREFORE
the probability that they are all boys can be eliminated as this is not possible and has probability ZERO.
there is still only one combination which produces all girls but now the total number of different possibilities has been reduced to seven.
CONCLUSION is that IN THIS PARTICULAR GIVEN SCENARIO there is a 1 in 7 chance of all 3 being girls.
JediTony.. you are a faggot..
Rajesh? Please start posting the solutions again. I mean look at this. Do you really want a repeat of Chicken Little?
did any one take into account the question relates to ducks, so therefore the equation would be entirely different depending on whether they were hatched in the same lot, how many survived and if they're anything like chickens, the poor boys would have been turned into stock before they'd barely took their first steps. Poor Huey and Duey.
Uncle Scrooge is not married. He is their great-uncle.
The probility is 1/8. one for the fact they might be boys, 3 for one of them beinga girl 3 differnet combinations of 2 of them being girls.Finally 1 for them all being girls. Add these all together and u get eight, simple
1/7 is the correct answer here.
P(A|B)=P(AnB)/P(B)
= (1/8)/(7/8)= 1/7
This sais that the probablity of one event A happening, given that B has already happend is the Probability of both events happening divided by the probability that B happens.
ANSWER 1/7
---------------------
Position does matters
There are 8 possibilities
bbb,bbg,bgb,bgg,gbb,gbg,ggb,ggg
bbb is not the case so that leave 1/7
GOT RIGHT
---------------------
bald, yujin, ben, -Ashley-, E the iching, chai, JediTony, Sir
me thinks u can look at this differently
like flipping a coin hds boy
tails girl
each flip is 50/50
1 girl - tails - known
prob = 50/50 and 50/50
for next 2 flips
so overall probability 4/1?
just seen ans in
posting anyhow
The possibilities are:
bbb,bbg,bgg,ggg,ggb,gbb,gbg,bgb
All 3 Girls means
P(all girls)+P(any girl)-P(no girl)
so,
(1/8)+(1/6)-(1/8)=16.67% chance or having all girls
Actually, it's 25%. That's because you all keep mentioning that 3 options are BBG, BGB and BGG... but that is not possible since you know you have G first. Therefore, you have GGG, GBG, GBB and GGB... so a 1/4 chance of all girls.
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