Sex of a newly added baby after drawing a boy

A room holds five babies, two boys and three girls. A sixth baby, equally likely to be a boy or a girl, is brought in. One of the six babies is then chosen at random and turns out to be a boy. What is the probability that the newly added baby is a boy?

$3/5$. If the newcomer is a boy, a random pick is a boy with probability $3/6$; if a girl, $2/6$. With equal priors, Bayes gives $\dfrac{3/6}{3/6+2/6}=\dfrac35$.