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# If a family has three children, what is the probability that the famil

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If a family has three children, what is the probability that the famil  [#permalink]

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25 May 2018, 04:24
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If a family has three children, what is the probability that the family has at least one girl?

A. 1

B. 0.875

C. 0.75

D. 0.50

E. 0.375

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Re: If a family has three children, what is the probability that the famil  [#permalink]

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25 May 2018, 05:03
1
Bunuel wrote:
If a family has three children, what is the probability that the family has at least one girl?

A. 1

B. 0.875

C. 0.75

D. 0.50

E. 0.375

The probability that all three children are boys is 0.5*0.5*0.5 = 0.125

The probability that the family has at least one girl is 1-0.125 = 0.875

Hence Option B = 0.875 is the answer.
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Re: If a family has three children, what is the probability that the famil  [#permalink]

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25 May 2018, 05:44
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Probability of having at least one girl =1- Prob of all boys
Prob of having all boys =0.5*0.5*0.5
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Re: If a family has three children, what is the probability that the famil  [#permalink]

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26 May 2018, 07:01
Probability of having atleast a girl= 1- Probability of having all boys

Probability of having a boy= 1/2
Probability of having three boys= (1/2)(1/2)(1/2) = 1/8

Probability of having atleast a girl = 1- (1/8) = 7/8 = 0.875

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Re: If a family has three children, what is the probability that the famil  [#permalink]

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29 May 2018, 09:16
2
Bunuel wrote:
If a family has three children, what is the probability that the family has at least one girl?

A. 1

B. 0.875

C. 0.75

D. 0.50

E. 0.375

The two events “at least one girl” and “no girls” are complementary events, which means that the sum of their probabilities is 1. Thus, we have:

P(at least 1 girl) = 1 - P(no girls)

P(no girls) = 1/2 x 1/2 x 1/2 = ⅛

So, P(at least 1 girl) = 1 - P(no girls) = 1 - 1/8 = 7/8 = 0.875.

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Re: If a family has three children, what is the probability that the famil  [#permalink]

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29 May 2018, 13:24
Bunuel wrote:
If a family has three children, what is the probability that the family has at least one girl?

A. 1

B. 0.875

C. 0.75

D. 0.50

E. 0.375

Total sample space = BBB,BBG,BGB,GBB,GGB,GBG,BGG,GGG where G=Girl and B=BOY

probability that at least one of the children will be girl = 7/8 = .875
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Re: If a family has three children, what is the probability that the famil  [#permalink]

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31 Jan 2019, 18:47
Bunuel wrote:
If a family has three children, what is the probability that the family has at least one girl?

A. 1

B. 0.875

C. 0.75

D. 0.50

E. 0.375

We can use the formula:

P(at least one girl) = 1 - P(no girls)

P(no girls) = (1/2)^3 = 1/8.

P(at least one girl) = 1 - 1/8 = 7/8 = 0.875.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: If a family has three children, what is the probability that the famil   [#permalink] 31 Jan 2019, 18:47
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