Elementary probability

Question

A box contains 3 black balls, 2 white balls... A ball is picked from the bag and then replaced, a second ball is chosen, what is the probability that 1. They are both black. 2. One is black and one is white. 3. At least one is black. 4. At most one is black

Answer 1

Probability of two blacks = 3/5 * 3/5 = 9/25

Probability of one black and one white = probability of black then white (3/5 * 2/5) + probability white then black (2/5 * 3/5) = 12/25

Probability of at least one black = probability of two blacks (9/25) + probability of one black and one white = (12/25) = 21/25

Probability at most one is black is probability of one black and one white (12/25) + probability of no blacks (2/5 * 2/5 = 4/25) = 16/25