How many sons
I. Mrs. Jones has two children. At least one is a boy. What are the chances that both are boys?
II. Mrs. Brown has two children. The younger one is a boy. What are the chances that both are boys?
II. Mrs. Brown has two children. The younger one is a boy. What are the chances that both are boys?
Labels: Probability
posted by Chris at
3:09 PM
5 Comments:
Off topic: Chris ...I believe you asked Ragknot how to post a link in a comment ... will you share the process with me?
I - One in Three (33%)
II - One in Two (50%)
Simon H. That's right. Are you going to say why?
There are four ways Mrs Jones can have 2 children:
(1) Girl then Boy
(2) Girl then Girl
(3) Boy then Boy
(4) Boy then Girl
I) Given the information that at least one child is a boy, we can rule out number (2) leaving three possibilities. Only one of these three is boy-boy so given this initial information, the odds of both children being boys is one in three.
II) We are told that the YOUNGER child is a boy in this case, which rules out options (2) and (4) leaving only 2 possibilities. Only one of these two is boy-boy so this time the odds are 1 in 2 of both children being boys.
This is a classic probability problem called the boy/girl paradox, which illustrates how counter-intuative conditional probability problems can be.
Simon H. Thanks you. That was a good explanation.
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