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A man visits a couple who have two children.One of them, a boy, comes in to the room. Find the probability p that other is also a boy

a) 1/3 b) 2/3 c) 1/2 d) 3/4

Correct Ans: a) 1/3

However I am getting answer as 1/2.My solution is as follows.

The couple has two children, hence the sample space is as follows.

B- Boy G - Girl

BB BG GG ( BG and GB mean the same thing as Girl,Boy), but it is already known that one is boy.So the sample space reduces to

BB BG

So now p is 1/2

Is there some mistake is my approach ?

  • 2
    Is this the same as this question: [In a family with two children, what are the chances, if one of the children is a girl, that both children are girls?](http://math.stackexchange.com/questions/15055/in-a-family-with-two-children-what-are-the-chances-if-one-of-the-children-is-a)2012-09-13
  • 0
    Actually your answer is right, but your approach is wrong: without any information BG is twice as likely as BB (and also as GG).2012-09-13
  • 1
    No it is not a duplicate; the events are dependent in the linked question, but they are independent (first child, other child) here.2016-10-02

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