Question

A bag contains 3 black balls 2 white ball a ball is taken from the bag and then replace a second ball is chosen what is the (a) probability that they are both black (b)one is black and one is white (c)at least one is black

Answer 1

since you are replacing the first ball
prob(both black) = (3/5)(3/5) = 9/25
prob(one black, one white) = 2(3/5)(2/5) = 12/25

prob(at least one black) = 12/25 + 9/25 = 21/25

check on last one: at least one black ---> 1 - prob(both white)
= 1 - (2/5)(2/5) = 1 - 4/25 = 21/25

also notice that 9/25 + 12/25 + 4/25 = 25/25 = 1 , as it should be