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April 17th, 2013, 10:39 PM   #1
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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?
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April 17th, 2013, 10:50 PM   #2
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The answer key is correct (if we assume that each child was fathered by an adult).
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April 17th, 2013, 11:28 PM   #3
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Re: An easy probability question

Quote:
Originally Posted by maxgeo
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}...
Why 1/2? Using the wrong sample space would give you 1/4

Unless you have your own sample space different from the ones offered?

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April 18th, 2013, 11:32 AM   #4
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Re: An easy probability question

Quote:
Originally Posted by agentredlum
Quote:
Originally Posted by maxgeo
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}...
Why 1/2? Using the wrong sample space would give you 1/4

Unless you have your own sample space different from the ones offered?


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.
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April 18th, 2013, 01:04 PM   #5
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Quote:
Originally Posted by maxgeo
If one child is a boy
The wording used was "there is a boy in this family", and this choice of wording was very deliberate. You are not told which child that boy is.
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