On the morning of January 1, a hospital nursery has 3 boys and some number of girls. That night, a woman gives birth to a child, and the child is placed in the nursery. The probability of the newborn being a boy is equal to that of it being a girl.
On January 2, a statistician conducts a survey and selects a child at random from the nursery (including the newborn and every child from January 1). The child is a boy.
What is the probability the child born on January 1 was a boy?