Show that if A and B are independent events, then the pairs A and and B, and and are also…

Show that if A and B are independent events, then the pairs A and and B, and and are also independent.  An experiment consists of picking one of two urns at random and then selecting a ball from the urn and noting its color (black or white). Let A be the event “urn 1 is selected” and B the event “a black ball is observed.” Under what conditions are A and B independent?