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A couple decides to have 4 children. If they succeed in havi

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A couple decides to have 4 children. If they succeed in havi [#permalink] New post 03 Aug 2013, 23:54
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A couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 2 girls and 2 boys?

(A) 3/8
(B) 1/4
(C) 3/16
(D) 1/8
(E) 1/16



I see that we can use combination rule here [4! / 2! (2!)]/2^4. What if the question was 1 girls and 2 boys? What will be the nominator?
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Re: A couple decides to have 4 children. If they succeed in havi [#permalink] New post 03 Aug 2013, 23:59
Expert's post
ksung84 wrote:
A couple decides to have 4 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 2 girls and 2 boys?

(A) 3/8
(B) 1/4
(C) 3/16
(D) 1/8
(E) 1/16



I see that we can use combination rule here [4! / 2! (2!)]/2^4. What if the question was 1 girls and 2 boys? What will be the nominator?


If that was the case, the question would be similar to arranging B,B,G -->\frac{3!}{2!}.
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Re: A couple decides to have 4 children. If they succeed in havi [#permalink] New post 04 Aug 2013, 00:07
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Since there is an equal probability of having a boy or a girl, Any possible combination of 4 children has a probability of 1/16. Now there are 4!/2!*2! ways of having exactly 2 boys and 2 girls... which is 6. So total probability of that event happening is 6*1/16 = 3/8 = A

The answer would not change for 2 boys and 1 girl

Which will be 3*1/8 = 3/8
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Re: A couple decides to have 4 children. If they succeed in havi [#permalink] New post 25 Dec 2013, 06:28
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Since probability that the couple will have a boy or a girl is 1/2, likelihood of having 2 boys and 2 girls is 1/2* 1/2 * 1/2 * 1/2 = 1/16

Now, 2 boys out of 4 can be chosen in 4c2 i.e 6 ways. Choosing 2 boys out of 4 leaves 2 girls, hence no additional selection of girls is required.

Finally, probability of choosing exactly 2 boys and 2 girls is 1/16 * 6 = 3/8.

Hope that helps.
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Re: A couple decides to have 4 children. If they succeed in havi [#permalink] New post 10 Aug 2014, 01:40
By fundamental counting principle,
Total No of out comes: 2^4 = 16

Total Desired outcomes: No of ways to arrange BBGG by MISSISSIPPI rule= 4!/(2!*2!) = 6

Probability is 6/16 = 3/8
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Re: A couple decides to have 4 children. If they succeed in havi   [#permalink] 10 Aug 2014, 01:40
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