You're in a hospital where your son was just born. As a nurse wheels your newborn into the nursery, she remarks that yours is the only boy in the room, and the rest of the babies are girls. Once in the nursery, boys are swaddled in blue blankets and girls are wrapped in pink.

A few minutes later, another baby is brought into the nursery and the baby's father, Tom, introduces himself to you. You couldn't see if his child was a boy or a girl, and before you get a chance to ask him, Tom has gone down the hall.

A few minutes later a baby, swaddled in blue, is brought out of the nursery.

What is the probability that Tom's newborn child is a boy?

I agree with 2/3 as well.
I'm often guilty of not reading problems carefully enough.  At first I read this as "A few minutes later a baby, swaddled in blue, is brought into the nursery."  I didn't see how it was answerable.

But what the situation really is is:

• a bunch of girls are in the nursery
  
• a boy added to the room - yours
• another baby is added to the room - Tom's (unknown gender)
• One of these babies is brought out of the nursery
• This baby is a boy
  
• We don't know whose baby this is
  

What's the probability Tom's is a boy?

One of the keys here is we don't know whose baby it is.

I'd also point out that Charlie's table also shows the probability that this baby is yours is 2/3.
This seems to be a coincidence.  If Tom's chance of having a son (beforehand) were somehow higher than 1/2 the chance that the boy brought out is Tom's would increase but the chance it is yours would decrease.

Posted by Jer on 2014-05-08 12:46:47