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

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Manager
Joined: 10 Oct 2005
Posts: 62
Followers: 1

Kudos [?]: 0 [0], given: 0

A couple wants four children. If the probability of having a [#permalink]  20 Oct 2005, 15:19
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?
VP
Joined: 22 Aug 2005
Posts: 1120
Location: CA
Followers: 1

Kudos [?]: 46 [0], given: 0

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
Manager
Joined: 10 Oct 2005
Posts: 62
Followers: 1

Kudos [?]: 0 [0], given: 0

agreed duttsit ans should be 6/16... but the ans provided is 5/16...
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
Followers: 23

Kudos [?]: 194 [0], given: 0

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
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