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fnumiamisburg
Joined: 10 Sep 2013
Last visit: 25 Jun 2019
Posts: 28
Given Kudos: 19
Location: United States
Concentration: Strategy, Operations
Schools: Fisher '16 Kelley '16 CUHK '16 Kellogg 1YR '15
GMAT Date: 12-10-2013
GPA: 3.5
WE:Operations (Manufacturing)
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?
Experts ----Help required. How to approach it?
Can we expect such type of question in GMAT?
14 Oct 2013, 17:08
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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
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
15 Oct 2013, 06:03
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fnumiamisburg
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).
