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What is the probability for a family with three children to

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What is the probability for a family with three children to [#permalink] New post 06 Feb 2011, 01:20
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

59% (01:23) correct 41% (00:20) wrong based on 22 sessions
What is the probability for a family with three children to have a boy and two girls (assuming the probability of having a boy or a girl is equal)?

A. 1/8
B. 1/4
C. 1/2
D. 3/8
E. 5/8
[Reveal] Spoiler: OA

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petrifiedbutstanding

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Re: Family with three children [#permalink] New post 06 Feb 2011, 01:52
Probability(1B,2G) = Favorable choices of having exactly 1B and 2G/Total number of Possiblities of sexes for 3 children

Let's do the sample set:

Represent Girls with G and Boys with B

3 children can have following possibilities of sexes

GGG - 3 girls
GGB - 2 girls one boy
GBG
GBB
BGG
BGB
BBG
BBB

Total possibilities of both sexes = 8

Number of choices where there are exactly 2 girls and 1 boy are:
GGB
GBG
BGG
=3.

Thus, probability = 3/8

Ans: "D"

This problem is similar to having exactly 2 heads in 3 tosses.

Alternate way;
The total number of possibilities = (Number of possible outcomes in each flip)^(Number of tosses) = 2^3=8

Likewise;
The total number possible sexes for 3 children = (Number of possible sex for each child)^(Number of children)
Number of possible sex for each child = 2 = (Boy or Girl)
Number of children = 3

Total possible sexes = 2^3 = 8

Possibilities to have exactly 2 Girls out of 3 child and 1 Boy out of remaining 1 Child:
=
C^{3}_{2}*C^{1}{1} = 3

Thus, probability = Favorable/total outcomes = 3/8.
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~fluke

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Senior Manager
Senior Manager
avatar
Joined: 19 Oct 2010
Posts: 274
Location: India
GMAT 1: 560 Q36 V31
GPA: 3
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Kudos [?]: 31 [0], given: 27

GMAT Tests User
Re: Family with three children [#permalink] New post 06 Feb 2011, 01:59
fluke wrote:
Probability(1B,2G) = Favorable choices of having exactly 1B and 2G/Total number of Possiblities of sexes for 3 children

Let's do the sample set:

Represent Girls with G and Boys with B

3 children can have following possibilities of sexes

GGG - 3 girls
GGB - 2 girls one boy
GBG
GBB
BGG
BGB
BBG
BBB

Total possibilities of both sexes = 8

Number of choices where there are exactly 2 girls and 1 boy are:
GGB
GBG
BGG
=3.

Thus, probability = 3/8

Ans: "D"

This problem is similar to having exactly 2 heads in 3 tosses.

Alternate way;
The total number of possibilities = (Number of possible outcomes in each flip)^(Number of tosses) = 2^3=8

Likewise;
The total number possible sexes for 3 children = (Number of possible sex for each child)^(Number of children)
Number of possible sex for each child = 2 = (Boy or Girl)
Number of children = 3

Total possible sexes = 2^3 = 8

Possibilities to have exactly 2 Girls out of 3 child and 1 Boy out of remaining 1 Child:
=
C^{3}_{2}*C^{1}{1} = 3

Thus, probability = Favorable/total outcomes = 3/8.


Thanks. This explanation is much simpler than the one in the source. I've been using the F/T rule in most of my previous problems.

But the explanation in the source confused me.
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Re: Family with three children [#permalink] New post 23 Feb 2014, 17:11
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Re: Family with three children   [#permalink] 23 Feb 2014, 17:11
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