The probability of having a girl is identical to the

Question

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

crackgmat750 · Accepted Answer

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

EMPOWERgmatRichC · Answer

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

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

prasun9 · Answer

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

GMATinsight · Answer

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

chetan2u · Answer

Hi,
prob of same gender= prob of boy+ prob of girl= 1/2*1/2*1/2 *2=1/4..
ans E

GMATinsight · Answer

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

longhaul123 · Answer

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??

MathRevolution · Answer

P(Girl) = P(Boy) =  \frac{1}{2}

Family with three children, what is the probability that all the children are of the same gender: All three are boys or All three are girls:

=>  (\frac{1}{2} * \frac{1}{2} * \frac{1}{2})  +  (\frac{1}{2} * \frac{1}{2} * \frac{1}{2})

=>  \frac{1 }{ 8}  +  \frac{1 }{ 8}  =  \frac{2 }{ 8}

=>  \frac{1}{4}

Answer E

Paras96 · Answer

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?

Let the probability of having a girl = P(G)
Let the probability of having a girl = P(B)

According to given question => P(G)+P(B)=1 (P(G)=P(B))
=> 2P(G) = 1
=> P(G) = 1/2 = P(B)

Now,
Probability of 3 boys = probability of 3 girls = (1/2)*(1/2)*(1/2)=1/8
Probability of 3 children of same gender = Probability of 3 boys + probability of 3 girls = 1/8 + 1/8 = 1/4

Hence E

DanTheGMATMan · Answer

Just verbalize the 2 situations:3 boys or 3 girls, and fill in the probabilities for each scenario:

https://www.youtube.com/watch?v=Fxn_YW2Zxpc

The probability of having a girl is identical to the

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