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gamjatang
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A couple wants to have 4 children. The probability of 24 Nov 2005, 05:24
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A couple wants to have 4 children.
The probability of giving birth to a boy and the probability of giving birth to a girl are same.
What is the probability that the couple will have 2 sons and 2 daughters?



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A couple wants to have 4 children. The probability of 24 Nov 2005, 05:36
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Is the answer 1/5?
I couldnt think of any method. So wrote the entire situation down.

It can be ssss / sssd/ ssdd/ sddd / dddd
5 cases.
So probability for ssdd is 1/5.
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GMATT73
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A couple wants to have 4 children. The probability of 24 Nov 2005, 06:57
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I get 3/8 in about 1min.

By simplified brute force:

bbbb
gggg
3b1g (4)
3g1b (4)
2g2b (6)

6/18--->3/8
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remgeo
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A couple wants to have 4 children. The probability of 24 Nov 2005, 07:23
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I just read Honhu's stick post for probability. Applying the formula there,

I get
C(4,2) * (.5)^2 * (.5)^2 = 3/8
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rianah100
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A couple wants to have 4 children. The probability of 27 Nov 2005, 08:25
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Order does not matter.
ans is (1/2)^4 = 1/16
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christoph
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A couple wants to have 4 children. The probability of 27 Nov 2005, 10:22
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3/18...

S S G G => prob is 1/16

S S G G => 4! ways to arrange but we have to divide by 2! * 2! b/c S and S and G and G are same. so 1/16*4!/(2!*2!).



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