I'm a bit confused how decision tree's select the variables to split. I know they splitt the data set through variable to get a more pure data set. But can it happend that some explenatory variables or some classes of a categorical variable that are not used in the construction of the tree because they dont improve the impurity of the data set are dropped out?
So do decision tree's perform a variable selection and can drop some variable that are not usefull for the precidion?