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805+ (Hard)|   Probability|      
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Abhishek009
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A couple has two children, one of whom is a girl. If the probability 23 Apr 2016, 10:56
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HKD1710
Thanks Abhishek009,

I went thru all those solutions and i still did not understand only the following:

Quote:
WHY do we consider BG, GB as two cases instead of ONE case only. We are not arranging here.
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I hope its clear with you now, in case of any doubt , please feel free to revert ( Because I know P&C and Prob Concepts are very confusing) !!

Happy Preparations

Abhishek
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A couple has two children, one of whom is a girl. If the probability 23 Apr 2016, 11:07
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Abhishek009
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Thanks Abhishek009,

I went thru all those solutions and i still did not understand only the following:

Quote:
WHY do we consider BG, GB as two cases instead of ONE case only. We are not arranging here.

I hope its clear with you now, in case of any doubt , please feel free to revert ( Because I know P&C and Prob Concepts are very confusing) !!

Happy Preparations

Abhishek
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Any explanation on that specific part i mentioned would bring clarity. :)
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A couple has two children, one of whom is a girl. If the probability 23 Apr 2016, 11:25
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HKD1710
WHY do we consider BG, GB as two cases instead of ONE case only. We are not arranging here.
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BG = Boy takes birth Before Girl

GB = Girl takes birth before Boy

PS: I know I might be contradicting my own theory of twins , but it is crucial to understand it this way. Even twins born on the same day may be few minutes apart


Does it help you anyway ?
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A couple has two children, one of whom is a girl. If the probability 23 Apr 2016, 11:38
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HKD1710


Any explanation on that specific part i mentioned would bring clarity. :)
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Hi,
Do not get into kids as B or G,try with another example
say there are two different flavours of icecream - V and C..
50% chances that one can pick either and eat..
we know he ate two and one was surely a V.. what is the probabilty that he had two vanillas, V..
he could have had VC or CV or VV
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A couple has two children, one of whom is a girl. If the probability 23 Apr 2016, 11:42
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Abhishek009
HKD1710
WHY do we consider BG, GB as two cases instead of ONE case only. We are not arranging here.

BG = Boy takes birth Before Girl

GB = Girl takes birth before Boy

PS: I know I might be contradicting my own theory of twins , but it is crucial to understand it this way. Even twins born on the same day may be few minutes apart


Does it help you anyway ?
Show more

well neither we need to apply the twin or age or any other theory. lets put it this way:

I am told that my neighbour has two child. one is girl another may be boy or girl. I went to my neighbour's house. here are the total case:

1. a boy opens the door (then other child as we already know is girl) hence - BG.
2. a girl opens the door. (then other child could be boy or girl )- hence (GB or GG)

This is why we have these three cases.

GG is favorable out of three. so 1/3.
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A couple has two children, one of whom is a girl. If the probability 23 Apr 2016, 11:44
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chetan2u
HKD1710


Any explanation on that specific part i mentioned would bring clarity. :)

Hi,
Do not get into kids as B or G,try with another example
say there are two different flavours of icecream - V and C..
50% chances that one can pick either and eat..
we know he ate two and one was surely a V.. what is the probabilty that he had two vanillas, V..
he could have had VC or CV or VV
Show more

Thanks chetan. Your assistance helps! Kudos :)
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A couple has two children, one of whom is a girl. If the probability 08 Sep 2017, 19:36
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TimeTraveller
Sample space = {bb,bg,gb,gg}

Favourable event = {gg}.

Since it's given that one of the child is a girl, the new Sample Space = {bg,gb,gg}.

So, probability = 1/3. Ans (C).
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Hi Bunuel,
If we consider above method, does it mean that the given probability of either boy or girl being 50% is not required to solve the problem?
And also can you please tell, the given probability translate into which of the below equations?:-
P(B U G)= 0.5
or
P(B) = P(G)= 0.5

*U = Union
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A couple has two children, one of whom is a girl. If the probability 30 Dec 2017, 01:05
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A couple has two children, one of whom is a girl. If the probability of having a girl or a boy is 50%, what is the probability that the couple has two daughters?

A. 1/8
B. 1/4
C. 1/3
D. 1/2
E. 2/3
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VERITAS PREP OFFICIAL SOLUTION:

While every bone in your body wants to say 1/2, that is not correct! This is tricky conditional probability and considering the different possibilities is the best way to get it correct. If the couple has 2 children then there are 4 possibilities: BB, BG, GB, GG.

If one of the children is a girl then only 3 possibilities remain: BG, GB, GG. Of those 3, only one is favorable to create 2 daughters (GG) so the answer is 1/3. Answer is (C )
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A couple has two children, one of whom is a girl. If the probability 12 May 2018, 04:59
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OFFICIAL SOLUTION
Solution: While every bone in your body wants to say 1/2, that is not correct! This is tricky conditional probability and considering the different possibilities is the best way to get it correct. If the couple has 2 children then there are 4 possibilities: BB, BG, GB, GG.
If one of the children is a girl then only 3 possibilities remain: BG, GB, GG. Of those 3, only one is favorable to create 2 daughters (GG) so the answer is 1/3. Answer is (C )
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A couple has two children, one of whom is a girl. If the probability 21 Sep 2018, 04:47
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chetan2u

But knowing One of them is a girl, shouldn't we remove BG from the possible cases.
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As the order isn't given here, we can't remove BG form the same set. All we may remove is BB, Boy and a Boy as this is an irrelevant answer option for us here.
As we already know that one of the Child is girl.
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A couple has two children, one of whom is a girl. If the probability 21 Sep 2018, 05:52
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Bunuel --- Need your help to shine some more light on this, if possible. (I know this post is very old)

How can we use the probability approach in this question?
I understand that one of the children is already a girl. The probability that the other child is a girl is 1/2.
How does that line of reasoning completely fail here?

Thanks in advance. I am trying to understand the probability approach better here but am failing.
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A couple has two children, one of whom is a girl. If the probability 08 Jan 2022, 01:43
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The answer is 1/3.

Let's consider the case that probability is 1/2, if one of the two child is a girl (as many argued). Please check what is the probability if the question has been that the eldest child is a girl, than also it would be 1/2 in your case. The two probabilities cannot be same.
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A couple has two children, one of whom is a girl. If the probability 08 Jan 2022, 02:15
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Probability of having DD =
DD/DB+BB+DD
=1/3

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A couple has two children, one of whom is a girl. If the probability 08 Jan 2022, 15:46
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For people who want to think that birth order doesn't matter, that BG is no different than GB, the the situation would be:

BB
BG/GB
GG

and you'd have to then acknowledge that the BG/GB scenario is twice as likely as BB or GG, and that BB and GG are equally likely.

So if probability of GG or BB are each X, then probability of BG/GB is 2X.

Being told that one child is a girl (not only one), then the probability of GG would be X/(X+2X)= X/3X = 1/3

Of course, if you examine this approach you would realize that you actually ARE considering birth order.

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A couple has two children, one of whom is a girl. If the probability 02 Jun 2023, 01:24
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Here is a simple approach for conditional probability problems:

Recall that in conditional probability, the entire probability space has been restricted.
What does this mean?
Consider the question.
The full probability space would be (for two children):
Boy, Boy
Boy, Girl
Girl, Boy
Girl, Girl


Now, we know that there is one girl - therefore we can remove Boy, Boy our space is now:

Girl, Boy
Boy, Girl
Girl, Girl

To get our desired (girl,girl) we have 1 case out of our restricted 3 cases. So 1/3.

Note that the order does matter - although the end result is the same (one girl and one boy) the event is different. It's like flipping a coin - heads tails and tails heads are a different sequence, and hence different events
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A couple has two children, one of whom is a girl. If the probability 11 Jan 2026, 23:27
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