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# If there is an equal probability of a child being born a boy

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Director
Joined: 22 Nov 2007
Posts: 807
If there is an equal probability of a child being born a boy  [#permalink]

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07 Sep 2009, 09:09
5
00:00

Difficulty:

45% (medium)

Question Stats:

61% (01:28) correct 39% (01:19) wrong based on 235 sessions

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If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 3 children have two children of the same sex and one of the opposite sex?

A. 1/3
B. 2/3
C. 1/4
D. 3/4
E. 3/5
Intern
Joined: 23 Aug 2009
Posts: 27

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07 Sep 2009, 11:24
1
marcodonzelli wrote:
If there is an equal probability of a child being born a boy or a girl, what is the probability that a couple who have 3 children have two children of the same sex and one of the opposite sex?

a. 1/3
b. 2/3
c. 1/4
d. 3/4
e. 3/5

Let boy be represented by B and girl by G.
The possible outcomes of two children of same sex and one of opposite sex can be:
BBG OR GBB OR BGB OR GGB OR BGG OR GBG
(1/2*1/2*1/2) + (1/2*1/2*1/2) + (1/2*1/2*1/2) + (1/2*1/2*1/2) + (1/2*1/2*1/2) + (1/2*1/2*1/2)
1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 = 6/8 = 3/4 (D)
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02 May 2011, 00:00
3
1
1- (1/8 + 1/8) 3 boys and 3 girls.
3/4.
Intern
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Joined: 22 Jan 2011
Posts: 37
Schools: IE- ESCP - Warwick

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02 May 2011, 00:49
2
Let's find the opposite probability. How many ways are there to have all the children from the same sex?

BBB
GGG

2 ways out of 8 outcomes (2^3). Attention to not forget this is the OPPOSITE Probability, so 1- 2/8= 6/8

Simplify and you get 3/4, answer D. Solved in 1 min 12, however I doubt this is a 700 question.
Intern
Joined: 13 May 2013
Posts: 10

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05 Aug 2013, 20:06
1
Two Chances: (two girls and one boy) or (two boys and one girl)
Probability of either boy or girl =1/2

Case 1: two girls and one boy
1/2^3 * 3!/2!=3/8
Case 2: two boys and one girl
1/2^3 * 3!/2!=3/8

Mutually exclusive events so 3/8+3/8 =3/4
Intern
Joined: 19 Jun 2014
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14 Aug 2014, 12:33
Probability = Probability of two children with same sex and one of the opposite sex.
(1/2)^2 + 1/2 = 1/4 + 1/2 = 3/4.

Wrong approach?
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Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
If there is an equal probability of a child being born a boy  [#permalink]

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15 Aug 2014, 00:06
No of ways of selecting a gender - 2C1
No of ways of selecting any 2 children out of 3 = 3C2
Total possible outcomes - 2^3 (each child can be either a girl or a boy)

Probability=2C1*3C2/2^3= 2*3/2*2*2=3/4
Ans=D
Current Student
Joined: 18 Jul 2013
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Location: Italy
GMAT 1: 600 Q42 V31
GMAT 2: 700 Q48 V38
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If there is an equal probability of a child being born a boy  [#permalink]

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15 Aug 2014, 04:23
1
2 different outcomes : GGB or BBG

GGB : $$(1/2)^3 * 3=\frac{3}{8}$$ (we multiply by 3 because there are 3 arrangements : BGG, GGB or GBG)

BBG : $$(1/2)^3 * 3=\frac{3}{8}$$ (same reason than above)

Answer $$= \frac{3}{8} + \frac{3}{8} = \frac{3}{4}$$
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Re: If there is an equal probability of a child being born a boy  [#permalink]

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22 Jun 2016, 08:11
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Re: If there is an equal probability of a child being born a boy   [#permalink] 22 Jun 2016, 08:11