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A couple wants four children. If the probability of having a

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A couple wants four children. If the probability of having a [#permalink] New post 20 Oct 2005, 16:19
A couple wants four children. If the probability of having a boy or girl is equal, then what is the probability that they will have exactly two boys and two girls?
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 [#permalink] New post 20 Oct 2005, 17:24
6/16 or 3/8

Assumption:
(a) Couple do not have twins/triplets...
(b) boy or gal birth is mutually exclusive

there can be 6 different ways couple can have 2B & 2G
4!/(2! * 2!)

each of these have probability: 1/2*1/2*1/2*1/2 or 1/16

therefore total probability = 6 * 1/16 = 6/16 = 3/8
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 [#permalink] New post 21 Oct 2005, 06:55
agreed duttsit ans should be 6/16... but the ans provided is 5/16...
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 [#permalink] New post 21 Oct 2005, 10:17
If you have exactly 2 girls, then you have exactly 2 boys. Using binomial distribution:
P(2 boys and 2girls) = 4C2(0.5)^2(0.5)^2 = 3/8
  [#permalink] 21 Oct 2005, 10:17
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