1. A sample of two balls is drawn from an urn containing two white balls and three red balls. Are the events "the sample contains at least one white ball" and "the sample contains balls of both colors" independent?
2. An urn contains two white balls and three red balls. A ball is withdrawn at random (without being replaced), and then a second ball is drawn. Are the events "the first ball is red" and "the second ball is white" independent?