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Ms. Barton has four children. You are told correctly that [#permalink]
02 Jun 2003, 11:55

Ms. Barton has four children. You are told correctly that she has at least two girls but you are not told which two of her four children are those girls. What is the probability that she also has two boys?

The answer is A.
Since we know for sure that there are at least two girls out of four children, the question can be rephrased as "what is the probability of having two sons out of two children?" Assuming that both son and daughter are equally likely, we have the answer as 1/4
QED

dont u think 4C3 and 4C4 shouldbeadded as that would mean 3 girls and 4 girls, which is not an option since outa 4 children 2 should be boys ? _________________

This is a tricky question boss. The initial statement Ms Barton has two girls misleads you. If she has 4 children and two are girls then definitely other two are boys ( assuming no in between ). This is indirect way of asking what is the probability that out of 4 children 2 are boys.

I hope it is clear.

Last edited by anandnk on 30 Jan 2004, 07:43, edited 2 times in total.

the answer is D because its soooo very simple....the probability that out of the other two children (we already know that two are girls) both are boys is 1/2 as in case of any one of the two being a girl the probability does not hold

Firstly I thought that it is A. But after anandk's explanations I have some doubt. But still don't understand his explanation fully.
We were told that 2 out of 4 children are girls. Which left us with the question " What is the probability of 2 of the rest children are boys.
Probability that 3d child is boy 1/2 so probability of 4th child is boy also 1/2. By using formula we got 1/2*1/2=1/4.

What you have find out is simple probabilty for *EXCATLY* 2 boys and
2girls out of 4 children.

What has been asked is to find conditional probability.
Condition: 4 children and atleast 2 are girls. In other words, there can be
2 boys and 2 girls, 3 girls and 1 boy and all 4 girls.

What has been asked is that
Out of the above mentioned combinations what is the probability of
getting 2 boys and 2girls.

In math teams,

P (2B&2G given that atleast 2 out of 4 are girls) =
Combination(2B & 2G ) / ( (comb(2B+2G) + comb(3G+1B) + comb(4G) )

Since we have to find out the P of 2 boys out ouf 4. We have only once possible combinations 2G and 2B. so we have 2 children to chose from and both of them have to sons

Re: Tricky!! - Probability [#permalink]
03 Feb 2004, 06:11

ABNY2002 wrote:

Ms. Barton has four children. You are told correctly that she has at least two girls but you are not told which two of her four children are those girls. What is the probability that she also has two boys?

(A) 1/4 (B) 3/8 (C) 5/11 (D) 1/2 (E) 6/11

This is a question that I submitted a long time ago.

Anand is correct.

This is a question in "conditional probability".

Two ways to solve it:

1) first reduce the "possible" set to match the condition. We know that barton must have at least two girls. Of the 16 possible arrangements of children from youngest to oldest, only 11 qualify. Hence there are 11 possible arrangement of kids. Of those 11 exactly 6 have 2 boys. Hence, the probability is 6/11.

2) The "formula" for conditional probability is "prob without the condition" divided by "the probabllity of the condition". Hence, the odds of getting exactly 2 boys and 2 girls out of the sixteen possible is: 6/16. (BBGG, BGBG, BGGB, GGBB, GBGB, GBBG.), The probability of the condition (at least 2 girls) is 11/16 (16 less 5: BBBB, BBBG, BGBB, BBGB, GBBB).

6/16 divided by 11/16 = 6/11. _________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993