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.