Before attempting this challenge, students must understand conditional probability. They must also know the basics of probability, such as the addition and multiplication rules. This challenge is difficult because it deals with conditional probability, which is often counterintuitive.

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?