*Tricky Probability Problem*

[BigShow]

Can anyone figure this out?


A new neighbour recently knocked on my door to borrow a cup of sugar. I asked if she had any children, she said "yes, I have three children, all in elementary school." Since I have two daughters, my next question was "Are any of your children girls?", to which she responded "Yes". The next day I saw her with a girl. I asked her if she was her daughter, to which she responded "Yes". What is the probability that this is my neighbour's only daughter?

[Kirbs17]

.125 or 12.5% ?

[BigShow]

Originally posted by Kirbs17
.125 or 12.5% ?

how do you figure?

[ricefarmer]

(1/2 x 1/2 x 1/2)

[Kirbs17]

Child 1= .50 boy, .50 girl
Child 2= .50 boy, .50 girl
Child 3= .50 boy, .50 girl

So First child boy, times second child boy, times third child girl = .50x.50x.50 = .125 or 12.5%


That may be completely wrong though. Its been ages since Ive done probabilities

[calgarygts]

25%

The probability that the remaining two children are boys is:

.50 X .50 = .25 or 25%.

This means that the probability that the daughter is the only female is 25%. Makes sense to me but I could be wrong (I think it's a multiplication but I don't really remember).

[calgarygts]

You guys are forgetting that the girl is a given, not a possibility. The probability is only if the remaining two children are boys or not.

[ricefarmer]

^^ gts is right, the question is asking what is the probablity that the last two children are boys (what is the probability she is the only daughter) so 25% is correct (50% x 50%)

[Audio_Rookie]

gts has got it....didnt even have to use any fucked up matrixes either....straight forward.

[Kirbs17]

Fuck... Right right right. Thanks for the reminder GTS

[BigShow]

hey guys, apparently gts isn't right...

the professor said this:

your solution could have some
faulty logic....

Let me just say this: does the neighbour have (i) exactly one girl
or (ii) at least one girl?????

so now i'm really confused...

[jasian]

how about 33%
there's 33% chance she has 1, 33% chance she has 2 and 33 she has 3..

haha i dunno..

[Audio_Rookie]

I dont get it....the professors point would be valid if we didnt already know she has 1 daughter....but since she does...it makes no sense.

even the simple matrix proves this....

25% chance all will be girls
50% chance there will be 2 girls and 1 boy
25% chance there will be 1 girls and 2 boys.

the only possibilities are.
girl, girl, girl = 1x.5x.5
girl, boy, girl = 1x.5x.5
girl, girl, boy = 1x.5x.5
girl, boy, boy = 1x.5x.5

2 of those situations have 2 girls and 1 boy, so we add them.

25% has gotta be it. are you in a logic class or an algebra class?


I cant really find anything fucked up in the original question......if there is something hidden in there its hidden deep....or its just worded so bad that no human should be able to understand it.

[Stratus_Power]

3/7 or 42.86%

[dennisaur]

i say it's 50%... it's either her only daughter or it's not hahaha

[DeeK]

you also have to take into account that girls are more common at birth, 56%. so chances that she has girls are slightly higher than if she had boys.

LOTS of little factors such as this, but for the sake of math I'll call it 50%

lol.

[DeeK]

Originally posted by dennisaur
i say it's 50%... it's either her only daughter or it's not hahaha
bingo.

[ricefarmer]

Originally posted by BigShow
hey guys, apparently gts isn't right...

the professor said this:

your solution could have some
faulty logic....

Let me just say this: does the neighbour have (i) exactly one girl
or (ii) at least one girl?????

so now i'm really confused...


theres nothing to be confused about since the question is asking this:
What is the probability that this is my neighbour's only daughter?
so to put it in other terms, the question is asking what is the probability that the remaining 2 children ARE BOYS
so gts is still right
im pretty sure thats right but see what your teacher says

[Stratus_Power]

Originally posted by DeeK


LOTS of little factors such as this, but for the sake of math I'll call it 50%

lol.


haha thats like say the chance of winning the Lottery is 50%, either you win the jackpot or you dont :P

[Hamann]

^:rofl: :rofl: Priceless

[PureDeXteritY]

I think Jasian is right with 33.3% or 1/3

Her remaining children at home are either
a.) boy + boy
b.) boy + girl
c.) girl + girl

In order for her neighbour to only have 1 daughter, her children at home must be a.)boy + boy, which is 1 out of 3 possibilities

[matt_calgary]

Don't you add up all the different combinations?

[BigShow]

Originally posted by PureDeXteritY
I think Jasian is right with 33.3% or 1/3

Her remaining children at home are either
a.) boy + boy
b.) boy + girl
c.) girl + girl

In order for her neighbour to only have 1 daughter, her children at home must be a.)boy + boy, which is 1 out of 3 possibilities

but it just seems like there has to be more than that...

this is due tommorow...lol im gonna try a new method here give me a minute

[Stratus_Power]

Originally posted by Stratus_Power
3/7 or 42.86%

Since Im in Genetic, this is my view:

All the possible combination :

MMM
FMM
MFM
MMF
FFM
FMF
MFF
FFF

Since one girl was spotted, we know for sure that It cannot be MMM.

so there are 7 possible scenario left, and 3 of them has only 1 Daughter.

so 3/7 or ~42%