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The probability of having a girl is identical to the

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The probability of having a girl is identical to the  [#permalink]

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New post 17 Sep 2004, 15:07
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The probability of having a girl is identical to the probability of having a boy. In a family with three children, what is the probability that all the children are of the same gender?

A. 1/8.
B. 1/6
C. 1/3
D. 1/5
E. 1/4
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Re: The probability of having a girl is identical to the  [#permalink]

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New post 17 Sep 2004, 16:42
2
1
1/4
There are two cases. All boys and all girls.
case 1. all boys.
1/2*1/2*1/2= 1/8
case 2 .all girls.
1/2*1/2*1/2=1/8
We will add the cases to get 1/4
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Re: The probability of having a girl is identical to the  [#permalink]

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New post 13 Apr 2015, 12:46
1
The 1st kid may be a boy or a girl, we are only concerned with the gender of the other 2 kids, which must be same as the 1st kid.
Hence the Probability that the gender of the 2 kids is same as the 1st kid = 1/2 * 1/2 = 1/4

Answer: E
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Re: The probability of having a girl is identical to the  [#permalink]

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New post 13 Apr 2015, 18:14
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Hi All,

The probability 'math' behind this question is fairly low-level, so most Test Takers could probably handle it without too much trouble. However, if you're not great at dealing with probabilities yet, the numbers involved in this question are so small that you could 'map-out' all of the possibilities. In that way, "brute force" can get you the correct answer rather quickly.

Since the probability of having a girl is identical to the probability of having a boy, we don't have to do anything special with the math. The possible outcomes for having 3 children are:

B=Boy, G=Girl

BBB
BBG
BGB
GBB

GGG
GGB
GBG
BGG

The question asks for the probability of having 3 children that are ALL the SAME gender (meaning all boys or all girls):

Total possibilities = 8
Total with 3 boys or 3 girls = 2

2/8 = 1/4

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PROBABILTY  [#permalink]

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New post 28 Jun 2015, 20:56
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The probability of having a girl is identical to the probability of having a boy. In a family with three children, what is the probability that all the children are of the same gender?

(A) 1/8
(B) 1/6
(C) 1/3
(D) 1/5
(E) 1/4
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Re: PROBABILTY  [#permalink]

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New post 28 Jun 2015, 21:07
campus1995 wrote:
The probability of having a girl is identical to the probability of having a boy. In a family with three children, what is the probability that all the children are of the same gender?

(A) 1/8
(B) 1/6
(C) 1/3
(D) 1/5
(E) 1/4


Probability of all three children to be Boy = (1/2)*(1/2)*(1/2) = 1/8
Probability of all three children to be Girl = (1/2)*(1/2)*(1/2) = 1/8

Probability of all three children to be Same gender = (1/8) + (1/8) = 1/4

Answer: Option E
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Re: PROBABILTY  [#permalink]

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New post 28 Jun 2015, 21:09
campus1995 wrote:
The probability of having a girl is identical to the probability of having a boy. In a family with three children, what is the probability that all the children are of the same gender?

(A) 1/8
(B) 1/6
(C) 1/3
(D) 1/5
(E) 1/4


Hi,
prob of same gender= prob of boy+ prob of girl= 1/2*1/2*1/2 *2=1/4..
ans E
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Re: PROBABILTY  [#permalink]

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New post 28 Jun 2015, 21:11
campus1995 wrote:
The probability of having a girl is identical to the probability of having a boy. In a family with three children, what is the probability that all the children are of the same gender?

(A) 1/8
(B) 1/6
(C) 1/3
(D) 1/5
(E) 1/4


ALTERNATE METHOD

Every Child has 2 possibilities of belonging to one of the two genders (i.e. boy or girl)

Total Out comes of Three Children to have any gender = 2 x 2 x 2 = 8

Favorable Outcomes of All children to have Same Gender = Either all boys (1case) or All girls(1 case) = 2

Probability = favorable Outcomes / Total Outcomes = 2/8 = 1/4

Answer: Option E
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Re: The probability of having a girl is identical to the  [#permalink]

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New post 28 Jun 2015, 23:26
campus1995 wrote:
The probability of having a girl is identical to the probability of having a boy. In a family with three children, what is the probability that all the children are of the same gender?

(A) 1/8
(B) 1/6
(C) 1/3
(D) 1/5
(E) 1/4


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Re: The probability of having a girl is identical to the  [#permalink]

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New post 09 Jul 2017, 04:05
P(G)=1/2 and P(B)=1/2 and the event can take place in 2 ways : GGG+BBB or BBB+GGG = (1/2)^3*2
= 1/8 *2 = 1/4. Am i correct in my understanding of the problem??
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