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?
We need only count the cases that involve the two fathers in the story. We know the baby is not someone else's:
Tom has nurse chose You'd see
son your baby blue
son Tom's baby blue
daughter your baby blue
daughter Tom's baby pink
In two out of the three cases where you see blue, Tom has a son.
The counterintuitiveness is that in two out of the three cases where you see blue, it's your baby, rather than Tom's. But realize that in half those cases, Tom also has a boy.
Posted by Charlie
on 2014-05-08 10:56:15