Mystery Gender II

A room contains $n_1$ baby boys and $n_2$ baby girls. A baby of unknown gender is added to the room, and then a baby is selected uniformly at random. The baby selected is a boy. At birth, it is known that a proportion $0 < p < 1$ of children are boys. Find the probability that the added baby was a boy when $n_1 = 5, n_2 = 3,$ and $p = 2/3$.