There are $15$ black balls and $10$ white balls in a box. Four balls are drawn randomly one after another without replacement. Please give the probabilities of the following events and show your reasoning in each case:

$1.$ Construct a probability tree of the problem.

$2.$ The first ball is black.

$3.$ The second ball is black.

$4.$ The first ball and the second ball are white.

$5.$ The second ball is white given that the first ball is black.

$6.$ All four balls are black.

$7.$ Getting two blacks and two whites in any order.