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Alex has five children. He has at least two girls (you do no

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fnumiamisburg
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Alex has five children. He has at least two girls (you do no [#permalink] New post   14 Oct 2013, 12:26
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Alex has five children. He has at least two girls (you do not know which two of his five children are girls). The probability of having a boy is 0.4 while the probability of having a girl is 0.6. What is the probability that he has at least two boys too?

Experts ----Help required. How to approach it?
Can we expect such type of question in GMAT?
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Bunuel
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Re: Alex has five children. He has at least two girls (you do no [#permalink] New post   15 Oct 2013, 06:03
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fnumiamisburg wrote:
Alex has five children. He has at least two girls (you do not know which two of his five children are girls). The probability of having a boy is 0.4 while the probability of having a girl is 0.6. What is the probability that he has at least two boys too?

Experts ----Help required. How to approach it?
Can we expect such type of question in GMAT?


We are told that Alex has at least two girls. 5 cases are possible:
GGBBB
GGGBB
GGGGB
GGGGG

We need to find the probability that Alex also has at least two boys. So, we need to find the probability that first two cases (in red) occurred out of 5.

P = P(at least 2 boys and at least 2 girls)/P(at least 2 girls).

P(at least 2 boys and at least 2 girls) = \(\frac{5!}{3!2!}*0.6^2*0.4^3+\frac{5!}{3!2!}*0.6^3*0.4^2\).

P(at least 2 girls) = 1 - (P(5 boys) + P(1 girl and 4 boys)) = \(1- (0.4^5+\frac{5!}{4!}*0.6*0.4^4)\).

I don't think that such kind of questions can ever appear on the real test (good for practice though).
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Re: Alex has five childerns [#permalink] New post   14 Oct 2013, 17:08
Looks like a case for binomial theorem.
Since we know at least two are girls, lets ignore that. The questions then is, what is the probability that two of three kids are boys.

Applying Binomial: 3.(0.6).(0.4).(0.4) = 0.288
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Re: Alex has five children. He has at least two girls (you do no [#permalink] New post   15 Oct 2013, 06:23
Thanx Bunel,

Is this a type of conditional probability?
Does GMAT includes it ? I have manhattan math book section, and I haven't came across conditional probability questions in it.
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Re: Alex has five children. He has at least two girls (you do no [#permalink] New post   15 Oct 2013, 08:59
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fnumiamisburg wrote:
Thanx Bunel,

Is this a type of conditional probability?
Does GMAT includes it ? I have manhattan math book section, and I haven't came across conditional probability questions in it.


Yes, it's a conditional probability question. Think we can expect simple conditional probability questions on the test.
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Re: Alex has five children. He has at least two girls (you do no [#permalink] New post   18 Nov 2013, 03:18
Bunuel wrote:
fnumiamisburg wrote:
Alex has five children. He has at least two girls (you do not know which two of his five children are girls). The probability of having a boy is 0.4 while the probability of having a girl is 0.6. What is the probability that he has at least two boys too?

Experts ----Help required. How to approach it?
Can we expect such type of question in GMAT?


We are told that Alex has at least two girls. 5 cases are possible:
GGBBB
GGGBB
GGGGB
GGGGG

We need to find the probability that Alex also has at least two boys. So, we need to find the probability that first two cases (in red) occurred out of 5.

P = P(at least 2 boys and at least 2 girls)/P(at least 2 girls).

P(at least 2 boys and at least 2 girls) = \(\frac{5!}{3!2!}*0.6^2*0.4^3+\frac{5!}{3!2!}*0.6^3*0.4^2\).

P(at least 2 girls) = 1 - (P(5 boys) + P(1 girl and 4 boys)) = \(1- (0.4^5+\frac{5!}{4!}*0.6*0.4^4)\).

I don't think that such kind of questions can ever appear on the real test (good for practice though).


please explain this,
why cant we simply go for the two cases of having 2 boys and 3 girls OR 3 boys and 2 girls ?
5C2 X [(0.4)^3 X (0.6)^2 + (0.4)^2 X (0.6)^3] ???
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Re: Alex has five children. He has at least two girls (you do no [#permalink] New post   24 May 2014, 09:36
Not tough, but little bit complex multiplication required.
GGBBB
10*0.6^2*0.4^3=0.2304
GGGBB
10*0.6^3*0.4^2=0.3456

SUM=0.2304+0.3456=0.576 Ans.
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Re: Alex has five children. He has at least two girls (you do no [#permalink] New post   26 May 2019, 12:14
fnumiamisburg wrote:
Alex has five children. He has at least two girls (you do not know which two of his five children are girls). The probability of having a boy is 0.4 while the probability of having a girl is 0.6. What is the probability that he has at least two boys too?

Experts ----Help required. How to approach it?
Can we expect such type of question in GMAT?


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Re: Alex has five children. He has at least two girls (you do no [#permalink]
26 May 2019, 12:14
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