  We investigate conditioning Galton-Watson trees on general recursive-type
events, such as the event that the tree survives until a specific level. It
turns out that the conditioned tree is again a type of Galton-Watson tree, with
different types of offspring and a level-dependent offspring distribution,
which will all be given explicitly. As an interesting application of these
results, we will calculate the expected cost of searching a tree until reaching
a given level.
