Expected Adjacent Boy-Girl Pairs in a Random Line

$b$ boys and $g$ girls stand in a line of length $b + g$, arranged uniformly at random. A "boy-girl position" is any pair of consecutive spots in the line where one person is a boy and the other is a girl. Find the expected number of boy-girl positions. As a concrete example, the arrangement $BGGBBGB$ (with $b = 4$, $g = 3$) has 4 boy-girl positions: $(B,G)$ at spots 1-2, $(G,B)$ at spots 3-4, $(B,G)$ at spots 5-6, and $(G,B)$ at spots 6-7. Evaluate your answer for $b = 10$ and $g = 15$.