Family 3 Children 2 Girls and 1 Boy
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What is the probability for a family with three children to take a boy [#permalink] 
Updated on: thirteen Mar 2019, 04:07
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What is the probability for a family unit with iii children to have a boy and two girls (assuming the probability of having a boy or a girl is equal)?
A. ane/8
B. 1/4
C. 1/2
D. 3/eight
East. 5/8
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Originally posted by petrifiedbutstanding on 06 Feb 2011, 01:xx.
Terminal edited by Bunuel on xiii Mar 2019, 04:07, edited ane time in total.
Renamed the topic and edited the question.
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Re: What is the probability for a family with three children to have a male child [#permalink] 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 prepare:
Represent Girls with K and Boys with B
3 children can have post-obit possibilities of sexes
GGG - iii girls
GGB - 2 girls 1 male child
GBG
GBB
BGG
BGB
BBG
BBB
Total possibilities of both sexes = eight
Number of choices where in that location are exactly 2 girls and 1 boy are:
GGB
GBG
BGG
=3.
Thus, probability = 3/viii
Ans: "D"
This problem is similar to having exactly 2 heads in iii tosses.
Alternate way;
The total number of possibilities = (Number of possible outcomes in each flip)^(Number of tosses) = ii^3=eight
Also;
The total number possible sexes for 3 children = (Number of possible sexual activity for each kid)^(Number of children)
Number of possible sex activity for each child = ii = (Boy or Girl)
Number of children = 3
Total possible sexes = two^3 = 8
Possibilities to have exactly ii Girls out of iii child and 1 Boy out of remaining 1 Child:
=
\(C^{3}_{two}*C^{one}{1} = 3\)
Thus, probability = Favorable/full outcomes = iii/eight.
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Re: What is the probability for a family with 3 children to have a boy [#permalink] 06 Feb 2011, 01:59
fluke wrote:
Probability(1B,2G) = Favorable choices of having exactly 1B and 2G/Full number of Possiblities of sexes for three children
Permit's practise the sample prepare:
Represent Girls with K and Boys with B
3 children tin have following possibilities of sexes
GGG - 3 girls
GGB - ii girls i boy
GBG
GBB
BGG
BGB
BBG
BBB
Total possibilities of both sexes = eight
Number of choices where there are exactly 2 girls and 1 male child are:
GGB
GBG
BGG
=three.
Thus, probability = iii/8
Ans: "D"
This problem is similar to having exactly 2 heads in three tosses.
Alternate way;
The total number of possibilities = (Number of possible outcomes in each flip)^(Number of tosses) = two^3=8
Likewise;
The total number possible sexes for 3 children = (Number of possible sex for each child)^(Number of children)
Number of possible sexual activity for each kid = 2 = (Boy or Girl)
Number of children = iii
Total possible sexes = 2^three = 8
Possibilities to take exactly 2 Girls out of 3 child and 1 Boy out of remaining 1 Child:
=
\(C^{3}_{ii}*C^{ane}{1} = 3\)
Thus, probability = Favorable/total outcomes = three/viii.
Cheers. This caption is much simpler than the one in the source. I've been using the F/T rule in near of my previous problems.
Simply the explanation in the source confused me.
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Re: What is the probability for a family unit with three children to have a boy [#permalink] 14 Sep 2014, x:33
fluke wrote:
Probability(1B,2G) = Favorable choices of having exactly 1B and 2G/Total number of Possiblities of sexes for three children
Let's do the sample set:
Represent Girls with Chiliad and Boys with B
3 children can take following possibilities of sexes
GGG - 3 girls
GGB - two girls one boy
GBG
GBB
BGG
BGB
BBG
BBB
Total possibilities of both sexes = viii
Number of choices where at that place are exactly ii girls and 1 boy are:
GGB
GBG
BGG
=iii.
Thus, probability = 3/8
Ans: "D"
This problem is similar to having exactly 2 heads in iii tosses.
Alternating way;
The total number of possibilities = (Number of possible outcomes in each flip)^(Number of tosses) = 2^three=viii
As well;
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 = ii = (Boy or Daughter)
Number of children = 3
Total possible sexes = ii^3 = eight
Possibilities to have exactly 2 Girls out of three child and ane Boy out of remaining 1 Child:
=
\(C^{three}_{2}*C^{1}{ane} = iii\)
Thus, probability = Favorable/total outcomes = three/viii.
Hello Fluke,
How does the combination of BGG and GBG vary? Why are we considering the order of kids here?
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Re: What is the probability for a family with 3 children to accept a boy [#permalink] 17 Sep 2014, 00:07
maggie27 wrote:
Howdy Fluke,
How does the combination of BGG and GBG vary? Why are we because the order of kids here?
Hello maggie27
Not Fluke, merely I may help.
A family has three children --> Let put the gild: C1_C2_C3 (child 1_child 2_child3).
Each child could exist boy or girl --> 2 means for C1; 2 ways for C2; two ways for C3. We have full 2x2x2 = viii means. It means you lot considered the order already i.e. BGB # BBG. Thus, when you count the combination (1boy, 2 girls), you lot have to consider the order. And so nosotros have iii orders that take one boy and ii girls
BGG; GBG; GGB
=> probability = 3/8
Hope information technology's clear.
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Re: What is the probability for a family with three children to have a boy [#permalink] 09 Jul 2017, 20:58
Since the probability of a boy and a girl are equal the individual probability is 1/ii and since there are BGG , (1/two)^3 * iii!/2! that is nosotros have to consider the arrangements = three/8. Hope this method helps
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Re: What is the probability for a family with three children to accept a boy [#permalink] 10 Jul 2017, 00:02
petrifiedbutstanding wrote:
What is the probability for a family with three children to have a male child and two girls (bold the probability of having a male child or a girl is equal)?
A. 1/8
B. 1/iv
C. 1/2
D. 3/8
East. 5/8
This can be solved in 2 ways.. First by checking number of events or 2d, by probability
First
Family to have a boy and 2 girls.
Total numbers of events possible i s
GGG
GGB
GBG
BGG
GBB
BGB
BBG
BBB
So, probability = iii/8.
Answer D.
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Re: What is the probability for a family with three children to have a male child [#permalink] 12 Jul 2017, 16:03
petrifiedbutstanding wrote:
What is the probability for a family with three children to take a male child and two girls (assuming the probability of having a boy or a girl is equal)?
A. ane/8
B. 1/four
C. ane/2
D. 3/8
E. five/8
We demand to determine the probability for a family with iii children to accept a boy and two girls.
P(Chiliad-Yard-B) = 1/2 x one/two x 1/2 = 1/8
We likewise see that there are three ways to adapt two girls and ane boy:
G-G-B
Grand-B-G
B-Thou-M
Thus, the probability is 1/8 ten 3 = 3/8.
Reply: D
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Re: What is the probability for a family with 3 children to have a male child [#permalink] xiii Mar 2019, 05:20
petrifiedbutstanding wrote:
What is the probability for a family unit with three children to have a boy and two girls (assuming the probability of having a boy or a girl is equal)?
A. 1/viii
B. one/4
C. one/2
D. iii/8
East. 5/8
A family tin can have a boy and ii girls in 3 means: BGG, GBG and GGB
The probability of getting each of these 3 ways is (ane/2)*(i/two)*(one/2) = i/8
So the probability of a male child and 2 girls = 3*(1/8) = 3/8
Answer (D)
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Re: What is the probability for a family with three children to take a boy [#permalink] 12 October 2020, fifteen:21
1/2 * i/2 * 1/ii = ane/viii
ane/8 * 3C2 = ane/8 * 3 = 3/viii
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Re: What is the probability for a family with 3 children to have a male child [#permalink] 26 Feb 2021, 10:40
VeritasKarishma wrote:
petrifiedbutstanding wrote:
What is the probability for a family with three children to have a male child and two girls (bold the probability of having a boy or a girl is equal)?
A. i/8
B. 1/4
C. 1/two
D. 3/eight
E. 5/8
A family can have a boy and 2 girls in 3 ways: BGG, GBG and GGB
The probability of getting each of these 3 ways is (1/2)*(one/2)*(1/2) = i/8
And then the probability of a boy and 2 girls = three*(1/viii) = three/8
Respond (D)
Hello, please tell me why social club matters hither ? Having BGG = GBG = GGB ? Please..
Re: What is the probability for a family with three children to have a boy [#permalink]
26 February 2021, 10:forty
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