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April 17th, 2013, 10:39 PM  #1 
Member Joined: Mar 2012 Posts: 60 Thanks: 0  An easy probability question
The probability question "a family that is known to have two children is selected at random from amongst all families with two children. Find the probability that both children are boys, given that there is a boy in this family." I think this is obviously 1/2 , but according to the answer key it's 1/3, explaining it as "the sample space changes from {BB BG GB GG} to {BB BG GB} because both children cannot be girls, therefore P(BB Not gg) = 1/3". What do you think? 
April 17th, 2013, 10:50 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,972 Thanks: 2222 
The answer key is correct (if we assume that each child was fathered by an adult).

April 17th, 2013, 11:28 PM  #3  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: An easy probability question Quote:
Unless you have your own sample space different from the ones offered?  
April 18th, 2013, 11:32 AM  #4  
Member Joined: Mar 2012 Posts: 60 Thanks: 0  Re: An easy probability question Quote:
Okay, If one child is a boy, then there is only one other child left to choose from. That child has a 50/50 chance of being a boy or a girl. Thus there is a 1/2 probability that the other child is a boy.  
April 18th, 2013, 01:04 PM  #5  
Global Moderator Joined: Dec 2006 Posts: 20,972 Thanks: 2222  Quote:
 

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