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child in a family

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child in a family

by sanju09 » Tue Mar 02, 2010 4:29 am
If at least 1 child in a family with 3 children is a boy, then what is the probability that the family has exactly 2 of the children as boys?
(A) 1/3
(B) 3/8
(C) 3/7
(D) 4/7
(E) 3/5
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by rohan_vus » Tue Mar 02, 2010 4:48 am
Atleast 1 is a boy among 3 children ,so total cases are

Family with 1 boy is BGG -->3 cases
Family with 2 boys is BBG --> 3 cases
Family with 3 boys is BBB -->1 case
Total cases = 7

So desired probability of exactly 2 boys is 3/7
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by sanju09 » Tue Mar 02, 2010 4:59 am
rohan_vus wrote:Atleast 1 is a boy among 3 children ,so total cases are

Family with 1 boy is BGG -->3 cases
Family with 2 boys is BBG --> 3 cases
Family with 3 boys is BBB -->1 case
Total cases = 7

So desired probability of exactly 2 boys is 3/7
[spoiler]IMO A[/spoiler]

Aren't (1 boy, 2 boys, and 3 boys) these three events equally likely?
The mind is everything. What you think you become. -Lord Buddha



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by rohan_vus » Tue Mar 02, 2010 5:22 am
On second thought , yes indeed !

You cant take BBB case ,as boys cant be indentical , obviously

Family with 1 boy is B1G1G2 -->6 cases
Family with 2 boys is B1B2G1 --> 6 cases
Family with 3 boys is B1B2B3 -->6 cases

Each event has 6/18 = 1/3 chances
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